Dr. P. GAYATHRI M.Sc., M.Phil., Ph.D. Assistant Professor, PG &Research Department of Mathematics
A.V.C COLLEGE (Autonomous),
Mannampandal, Mayiladuthurai -609 305.
2020
CERTIFICATE This is to certify that this project work was done under my guidance and the
dissertation entitled "A STUDY ON TRANSPORTATION PROBLEMS ON HEPTAGONAL FUZZY NUMBERS" Submitted by
B. BARANIDHARAN (Reg.No.P187101)
in partial fulfillment of the requirements for the award of Degree of Master of Science in Mathematics during 2018-2020 is the original work of the candidate.
BBoalu Signature of the Candidate P.Gyo
SIgnature ofthe Guid
(B.BARANIDHARAN) (Dr. P.GAYATHRI)
Dr.P.GAYATHRI, M.Sc. MP
ASSISTANT PROFESS PG &Research Department of Ma A.V.C. College (Autonomous) Mar
MAYILADUTHURAI, South Indi au
Signatureof theHead of the Department
0
Dr.S.GOVINDARAJAN,M.Sc,M.Phil.Ph.D. Head and Associate Professor,
Department of Mathematics A.V.C. College (Autonomous).
Mannampandal-609 305.
Signatúre of the External Examiner
Dr.S. SENTHILKUMAR, M Sc.M. Phil., Fh.D, Assistant Professor in Mathhema ic PG Department of Mathemat CS,
A.V.C. College (Autonomous MAYILADUTHURAI - 609 325.
Dr. C. JAISANkAR M.Se.,M.Phil.,Ph.D., MBA. Assistant Professor of Mathematies. A.V.C.COLLEGE (Autonomous). Mannanmpandal-609 305. Mayiladuthurai.
CERTIFICATE
This is to certify that the project work was done
A under nmy guidance and the dissertation entitled "4
HISTORY OF THE PRIME NUMBER THEORE.M"
submitted by P.HARISH, (Reg. No. P187102) in partial
fulfilment of the requirements for the award of the Degree
of Master of Science in Mathematics during 2018-2020 is
the original work of the candidate.
P lt Signature of the candidate Signature of the Guide
Signature of the Head of the Department Dr.S.GOVINDARAJAN,MSc MPhi Ph.D
Head and Associate Protessor, Department of Mathematics,
AVC. College (Autonomous).
Mannampandal 609 305.
Signature of the External Examiner Dr.S. SENTHILKUMAR, M Sc. M PhdF
AssistaHt Professor in NMuthema ie
PG Department of Mathemat c,
A.VC. Coliege (AutononiOu MAYILADUTHURAI -609
Dr. S. SENTHILKUMAR, M.Sc., M.Phil., Ph.D.,
Assistant professor of Mathematics, A.V.C COLLEGE (Autonomous), Mannampandal - 609 305
Mayiladuthurai.
CERTIFICATE
This is to certify that the project work was done under my
guidance and the dissertation entitled " A STUDY ON APPLICATION
OF QUADRATIC FORMS IN CRYPTOGRAPHY " submitted by
M. LAKSHMANAN, (Reg. No. P187103) in partial fulfilment of the
requirements for the award of the Degree of Mater of science in
Mathematics during 2018 - 2020 is the original work of the candidate.
mluwmelalano CSignature of the Guide
Signature of the Candidate V
Signature of théleal bf the Department
o Dr.S.GOVINDARAJAN,M Sc,M.Phi,Ph.
Head and Associate Professor, Department of Mathematics,
A.V.C. College (Autonomous),
Mannampandal-609 305.
Signature of the Exter^al EKaminer
DI$.AWINDARAJANRS MP.D
Hes1 na Associate
Protessor,
Departrent of Mathematics,
A.VC. College (Autenomous),
Mannampandal-609 305.
SOE 6091epuedweuue IRSOOIPNDARAJANMSC., M.Phil.Ph.D
$OMRHd JAsBanie tsgtesso
JOSsajbb aatINAtsyt NiattPPNDATICS,
O'd HdW 9WNDU
PaWANINOSI
305. Mannampandal-60
Dr. S. VEERAMANIKANDAN M.Sc., M.Phil., Ph.D. B.Ed., Assistant Professor of Mathematics. A.V.C.COLLEGE (Autonomous). Mannampandal-609 305. Mayiladuthurai.
CERTIFICATE
This is to certify that the project work was done
under my guidance and the dissertation entitled "A STUDY ON
NEGIBOURHOOOD CONNECTED MA.JORITY
DOMINATION IN GRAPHS" submitted by P.RANJITH.
(Reg. No. P18 7104) in partial fulfilment of the requirements for
the award of the Degree of Master of Science in Mathematics
during 2018-2020 is the original work of the candidate.
Veanaanwleada.nalegaest Signature of the candidate Signature of the Guide
Signature okthe Head of the Department Signature of the Examinèr Dr.S.GOVINDARAJANMSc.MPil.Ph.D,
Head and Associate Professor,
Department of Mathematics,
A.V.C. College (Autonomous).
Mannampandal-609 305
Dr.S. SENTHILKUMAR, M.Sc. M.Phil., Fh Assisranr Professor in Mathema ie PG Department of Mathemat.cs,
A.V.C. College (Autonomou3 MAYILADUTHURAI -609 305.
Dr. S.SASSICALA M.Sc., M.Phil., Ph.D., M.Ed., PGDCA, SLSI.
Assistant Professor, PG & Research Department of Mathematics A.V.C.COLLEGE (Autonomous), Mannampandal-609 305.
Mayiladuthurai. CERTIFICATEE
This is to certify that this project work was done under my
guidance and the dissertation entitled "A STUDY ON TRIANGULAR
FUZZY NUMBERS AND IT'S APPLICATIONS" submitted by
S.THIYAGU(Reg.No. P187105) in partial fulfilment of the requirements
for the award of the Degree of Master of Science in Mathematics during 2018-
2020 is the original work of the candidate.
b.FaOe 9)222 S.h SignatuYe of the candidate Signature of the Guide
S. SASSICALA Msc.M.Phil, SLST, M.Ed. PGOCA Assistant Professor
P.G&Research Department of Mathematics A.V.C. Colege (Autonomous),
Mannampandal 609 305.
Signaturé tNe Head of the Department Dr.S. GOVINDARAJAN,M.Sc.M.Phil.Ph.D,
Head and Associate Protessor, Department of Mathematics,
A.V.C.College (Autonomous), Mannampandal-609 305.
Signature of the ExternakExaminer
Dr.S. SENTHILKUMAR, M Sc. M.Phil, F , Assistant Professor in Mathenma ic PG Department of Mathemat cs,
A.V.C. College (Autonomou's MAYILADUTHURAI - 609 35.
Dr. J. PERIASWAMY, M.Sc., M.Phil., Ph.D., SET ASSISTANT PROFESSOR OF MATHEMATICS, A.V.C.COLLEGE (Autonomous). MANNAMPANDAL-609305.
CERTIFICATE
This is to certify that the project work was done by
ny guidance and the dissertation entitled "A STUDY ON ODD
GRACEFUL LABELING OF SOME GRAPHS" submitted
by B.VISHAL, (Reg. No. P187106) in partial fulfilment of the
in requirements for the Degree of Master of Science in
Mathematics is the original work of the candidate during the
academic period 2018-2020.
Signature of the candidate Signature of the Guide J.PERIASWAMY,
M.Sc, M.Ph., MISTE..
ASSISTANT PROFESSOR
DEPARTVENT OF MATHEMANICS
AV.C. COLLEGE (Autonemous MANNAMEMNDAL-809 305
AYHLADUTHURA
Signature of the Head of the Department
Dr.S.GOVINDARAJAN,M.Sc.M.Phil.PhD.
Head and Associate Professor,
Department of Mathematics, A.V.C. College (Autonomous),
Mannampandal-609 305.
Signture of the External Examiner
Dr.S. SENTHILKUMAR, M S., M Phil, Fh D
Assistanr Projessor in Mathema ic
PG Department of Mathemat.cs,
A.V.C. College (Autonomous
MAYILADUTHURAl -609 305
Dr. K. JAIKUMAR, M.Sc., M.Phil., Ph.D., Assistant Professor,
PG & Rexearch Department of Mathematles, A.V.C College (Autonomous),
Manuamunudal, Mayilauuthrai -009 305 Date: 18 9 2-
CERTIFICATE
This is to certify that this project entitled "A STUDY ON
TRANSPORTATION PROBLEM AND ITS VARIENTS" was donc under
my guidance and the dissertation Submitted by S. ANGAVAI(Reg. No: Pi18
7126) in partial fulfilment of the requirements for the award of the Master of
Science in Mathematics during 2018 - 2020. It is the original work of
candidate.
Signature of Hhe Candidate ignature of the Guide
(S. ANGAVAI) (K. JAIKUMAR) Dr.K.JAIKUMAR,M Se M Phit Ph D
Assistant Professor & Re earch Advi :or, Department of flate cS,
A.V.C.Colage (Auaa) Mir pandal, MayiladulhUrai-0930), Tann ad, Guth Inda.
Signaturt of yhe flead of the Department AA Signature of the External Examinér
Dr.S.GOVINDARAJAN,M.SC. M.Phil,Ph.D, Head and Assoçiate Professor,
Department of Mathematics,
AVC. College (Autonomous) Mannampandal.609 305
Dr.S. SENTHILKUMAR, M.Sc M Phil Fh , Assistant Professor in Muthema ic
PG Department of Mathemat cs, A.VC. College (Autonomous MAYILADUTHURAl 609 9 .
Dr. S. GoVINDARAJAN, M.Sc., M.Phil., B.Ed., Ph.D., Head and Associate Professor,
A.V.C. College (Autonomous)Mannampandal, MayiladuthuraiDate: 21.09. 2.02o Department of Mathematics.
CERTIFICATE
This is to certify that this project work was done by Miss.
K.ANUSHA (Reg.No: P187127) under my guidance and this dissertation
entitled 'Hyper graphs and Hyper groups' Submitted by her in partial
fulfillment of the requirements of Master of Science Degree in Mathematics for
the academic year 2018-2020 is the original work of the candidate.
. dnusla
Signature of the Candidate
(Miss. K. Anusha)
Signaturé df the Guide
(Dr. S. Govindarajan)
Signature of the
External Examiner
2l/1|20
Sigsturé of the Head of the Department
Dr.S. SENTHILKUMAR,
M.Sc M Phil, Fh D
Assistant
Professor in
Marlhema ic
PG Department
of Mathemat
cCS,
A.VC. Coliege (Autonomou MAYILADUTHURAI-609 303.
Dr.S. GOVINDARAAN,M.Sc.M Phil.Ph D
Head and Associate Protessor,
Department of Mathematics,
A.V.C. College (Autonomous), Mannampandal-609 305.
Dr. A. Yamuna, M.Sc., M.Phil., Ph. D., SET,
Assistant Professor of Mathematics, A. V. C. College (Autonomous), Mannampandal - 609305.
CERTIFICATE
Date: 18.9.2
This is to certify that the project work was done under my guidance
and the dissertation entitled A STUDY ON VARIANCE
RESIDUAL LIFE FUNCTION IN RELIABILITY STUDIES"
submitted by R. Anushya, (Reg. No. P18 7128) in partial fulfilment
of the requirements for the degree of Master of Science in
Mathematics is the original work of the candidate during the
academic year 2019- 2020.
M A R.Anushya. Signature of the candidate Signature of the Guide
Dr. A.YAMUNA,M.Sc.M.Phil, SET. Ph.D. Assistant Professor,
PG &Research Department of Mathematics A.V.C. College (Autonomous), Mannampandai,
Mayiladuthurai, South India-609 305.
Signafure of the Signature of the
Head of the Department External Examiner Dr.S.GOVINDARAJAN,MSC, MPhil. Ph.D.
Head and Associate Professor,
Department of Mathematics,
A.V.C. Coliege (Autonomous).
Mannampandal-609 305
Dr.S. SENTHILKUMAR, M.Sc. M.Phil, F D
Assistant Professor in Marhiema ic
PG Department of Mathemat c, A.V.C. Coll�ge (Autonomouu
MAYILADUTHURA - 609 305.
Dr. U. ARI NARAYANAN M.Se., M.Phil., P.G.D.C.A., Ph.D.
Assistant Professor,
P.G& Research Department of Mathematics, A.V.C. College (Autonomous)
Mannampandal, Mayiladuthurai -609 305
2020.
CERTIFICATE
This is to certify that this project entitled "A STUDY ON FUZZY SOFT SET AND ITS APPLICATIONS" was done under my guidance and the
dissertation Submitted by K. KAVI THENDRAL (Reg. No: P18 7130) in
partial fulfilment of the requirements for the award of the Master of
Science in Mathematies during 2018 2020. It is the original work of
candidate.
K.KovTherdhal Signature of the Candidate
Cl Signature of the Guide
(K. Kavi Thendral) (Dr.U.Hari Narayanan)
a Signature ofthe Nead of the Department Signatúre of the External Examíner\
Dr.S. GOVINDARAJAN,MSc
M Phil.Ph D,
Head and Associate Professor
Department of Mathematics,
A V.C College (Autonomous).
Mannampandal-609 305.
Dr S. SENTHILKUMAR, M Sc M. Phil F Asssttur P'rofessor in Mathemt i PG Department of Mathemat c,
AVC Colege (Autonom MAYILADUTHURAI-
Dr. N. MOHANA, M.se., M.Phil., SET, B.Ed., Ph.D., Assistant Professor of Mathematics A.V.C. College (Autonomous), Mannampandal - 609 305. Mayiladuthurai.
CERTIFICATE
This is to certify that this project work was done under my guidance and the
dissertation entitled "A STUDY ON THE KRONECKER SUM AND
PRODUCT " submitted by
R. KEERTHIKA (Reg. No. P18 7131)
in partial fulfilment of the requirements for the award of the Degree of Master of
Science in Mathematics is the original work of the candidate during the academic
period 2018- 2020.
N-Moka Signature of the Gaide
sta. Signature of the Candidate
Assia PC. Tmiatics
tofl .natics, A oiere (Auto mous), Mannamoarai-f"9 305, Mayiladuihurai.
Signaturèof the Head of the Department
23turd eW
Dr.S. GOVINDARAJAN,M.SC.M.PhilPh.D
Head and AssoCiate Protessor,
Department of Mathematics,
A.V.C. College (Autonomouss).
Mannampandal-609 305.
Signature of the External Examiner
Dr.S. SENTHILKUMAR, M Sc.M Phil,Fh.D AssistaHr Professor in Mathema ic PG Department of Mathematcs,
A.V.C. College (Autonomous MAYILADUTHURAI - 609 305.
Dr. A. Yamuna, M. Sc., M. Phil., Ph. D., SET Assistant Professor of Mathematics, A. V. C. College (Autonomous). Mannampandal - 609305.
CERTIFICATE
Date: 18.9.2o
This is to certify that the project work was done under
my guidance and the dissertation entitled A STUDY ON
ESTIMATION OF MEAN RESIDUAL LIFE FUNCTIONS"
submitted by P. Priyadharshini, (Reg. No. P187132) in partial fulfilment of the requirements for the Degree of Master of
Science in Mathematics is the original work of the candidate
during the academic year 2019- 2020.
Signature of the candidate Signature of the Guide Dr. A.YAMUNA,M.Sc. M.Phil., SET., Ph.D. Assistant Professor, PG&Research Department of Mathematics, A.V.C. College (Autonomous), Mannampandal, Mayiladuthurai, South India-609 305.
Signánre of the Signature of the Head of the Department External Examiner Dr.S. GOVINDARAJAN,M Sc.M.Phil.Ph.D.,
Head and Associate Professor,
Department of Mathematics, A.V.C. College (Autenomous).
Mannampandal-609 305.
Dr.S. SENTHILKUMAR, M.Sc. M.Phil,Ph.., Assistanr Professor in Mathenma ics,
PG Department of Mathemat cs, A.V.C. College (Autonomous MAYILADUTHURAI - 609 305.
Dr.A.GOVINDARASU M.Se., M.Phil., B.Ed.,Ph.D., Associate Professor and Head, PG &Rescarch Department of Mathematics.
A.V.C.College(Autonomous), Mannampandal-609305, Mayiladuthurai. 2020.
CERTIFICATE This is to certify that this project work was done under my guidance and the dissertation
entitled "CHARACTERIZATIONS OF SECONDARY NILPOTENT MATRICES "
submitted by M. SHERLY ABINAYA (Reg. No. P18 7133) in partial fulfilment of the
requirements for the award of the Degree of Master of Science in Mathematics during 2018
2020 is the original work of the candidate.
MBuls Amau A -Signature of the Candidate Signature of the Guide
Signature offl}e Nead of the Department
Dr. S. GOVINDARAJAN,M.Sc.M.Phil.,Ph.D., Head and Associate Professor,
Department of Mathematics,
A.V.C. College (Autonomous), Mannampandal-609 305.
Signature of the External Examiner
Dr.S. SENTHILKUMAR, M.Sc.,M. Phil, Fh.D., Assistant Professor in Matlhema ics,
PG Department of Mathemat.cs,
A.V.C. College (Autonomou3, MAYILADUTHURAl 609 305.
Mr. M. KANDAKUMAR M.Sc., M.Phil., B.Ed.,
Assistant Professor,
PG & Research Department of Mathematics
A.V.C. COLLEGE (AUTONOMOUS)
MANNAMPANDAL,
MAYILADUTHURAI - 609 305.
2020.
CERTIFICATE
This is to certify that this project entitled "A STUDY ON TRIANGULAR
FUZZY TRANSPORTATION PROBLEMS" was done under my guidance
and the dissertation Submitted by V.THAVASELVI (Reg. No: P18 7134)
partial fulfillment of the requirements for the award of the Master of Science
in Mathematies during 2018-2020. It is the original work of the candidate.
Signature of the Candidate Signature of the Guide
wUUVeo Signature of the External Ex�miner Signature of uNHead of the Departme
Dr.S.GOVINDARAJAN,M.Sc.MPhl, Ph D Head and Associate Profesor,
Department of Mathem.itics,
A.V.C.College (Autonomuus) Mannampandal-609 305
Dr.S. SENTHILKUMAR, M.Sc, MPhil., Fh.) Assistanr Professor in Marhena ie PG Department of Mathematcs,
A.V.C. College (Autonomous MAYILADUTHURAI - 609 305.
Mr. T. RAGAVAN, M.Sc., M.Phil., A.V.C.COLLEGE(Autonomous) Assistant Professor of Mathenatics, Mannampandal,
Mayiladuthurai - 609 305.
2020 Department of Mathematics.
CERTIFICATE
This is to certify that this project work was done under my guidance and the
dissertation entitled "A STUDY ON WIENER NUMBER AND THE DETOUR
SPECTRUM OF THE GRAPH" submitted by
V. ABINAYA (Reg. No. P187826)
In partial fulfillment of the requirements for the award of the Degree of Master of
Science in Mathematics during 2018 -2020. It is the original work of the candidate.
Abunaya 22 lo9 l2020 Signature of thë Candidate Signature of the Guide
Signature ofthe/Head of the DepartmenthD, Dr.S. GOVINDAX
Head and Associate
Protessor,
Department of Mathematics.
A.V.C.College (Autonomous
Mannampandal-609 305
Signatureof the Examiner
Dr. R. ANURADHA, M.Se., M.Phil., Ph.D., A.V.C.COLLEGE, (Autonomous)
Assistant Prolessor of Mathematics, Mannampandal, Mayiladuthurai 609 305.
24.9 2020
CERTIFICATE
This is to certify that this project work was done under my guidance and
the dissertation entitled "A STUDY ON FUZZY sQUARE MATRICES "
submitted by
G. ABIRAMI
(Reg. No. P187827)
in partial fulfillment of the requirements for the award of the Degree of Master
of Science in Mathematics during 2018 - 2020. It is the original work of the
candidate.
Aitami Signature of the Candidate Signature of the Guide
sighnte of the Signature of the
Head of the Department Dr. S. GOVINDARAJAN.MSc M Ch Dh
Head and Associate Protes sor Department of MathematiC.
A VC College tAutonomous Mannampandal-409 308
External Examiner
U. PRIYANKA, M.sc., M.Phil. A.V.C.College (Autonomous), Assistant Professor of Mathematics Mannampandal
May1laduthurai 609 305
2020
CERTIFICATE This is to certify that this project work was done under my guidance and the
dissertation entitled A STUDY ON VARIOUS GRAPH ENERGY OF GRAPHS" submitted by S. AGALPRIYA (Reg. No. P187828) in partial fulfillment of the
requirements for the award of the Degree of Master of Science in Mathematics dur1ng 2018-2020 is the original work of the candidate.
Signature of the Candidate Signature hf the Guide
Signature of'thé iAN of hs ReBREYANSM Se MPN Ph 0 Head and Associate Protessor
Department of Mathematics. AVC Coilege (Autonomous
Mannampandal 609 305
SignaturdGT Hhe Examiner
Dr. R. ANURADHA, M.Se. M.Phil. Ph.D. A.V.C.COLLEGE, (Autonomous) Assistant Professor of Mathematics. Mannampandal,
Mayiladuthura 05 2020
CERTIFICATE
This is to certify that this project work was done under my guidance and
the dissertation entitled "A Study on Min and Max matrices" submitted by
A.ATCHAYA
(Reg. No. PI87829)
in partial fulfillment of the requirements tor the aw ard of the Degree ot Master
of Seience in Mathematics during 2018 2020. It is the or1ginal work of the
candidate.
Aca Signature of the Candidate Signature of the Guide
20
Signature of the Sigturev the Head of the Department External Examiner
Dr S. GOVINDARAJAN,MSc M Phi PhD.
Head and Associate Professor,
Department of MathematiCs
AVC College (Autonomous, Vannampandal 609 305
Mrs.S.AARTHY, M.Sc., M.Phil.B.Ed. A.V.C.COLLEGE Assistant Professor of Mathematics (Autonomous)
Mannampandal, Mayiladuthurai - 609 305.
2020.
CERTIFICATE
This is to certify that this project work was done under my guidance and the
dissertation entitled" A STUDY ON INTERVAL MATRICES " submitted by
N.BIRUNDHA
(Reg.No. P187830)
in partial fulfillment of the requirements for the award of the Degree of Master of Science in Mathematics during 2018 2020. It is the original work of the candidate.
N Bu Signature of the Candidate Signature of the Guide
Signature of the He4d6f the Department Dr.S. GOVINDARAJAN,M Sc,M Phil,Ph.D.
Head and Associate Professor, Department of Mathematics,
A.V.C. College (Autornomous), Mannampandal-609 305.
Signatuke df the Examiner
Dr.B.ARTHI,M.Se.,M.Phil.,Ph. D. A.V.C.COLLEGE(Autonomous) Assistant Professor of Mathematics, Mannampandal.
Mayiladuthurai 609 305
2020
CERTIFICATE
This is to certily that this project work was done under my guidance and the dissertation
entitled"A STUDY ON DOUBLY STOCHASTIC MATRIX" submittedby
R.DHANALAKSIMI (Reg.No. P187831)
In partial fultillment of the requirements for the award of the Degree of Master of Science
in Mathematics during 2018 2020. It is the original work of the candidate
Signature of the Candidate Signature of fhe Guide
192
Signature of the FTend of the Department Dr. S. GOVINDARAJAN,M Sc Phd Ph
0
Head and AssoCiate Professor, Department of Mathematics,
AVC College (Autonomous).Mannampandal 609 305
Signátutohe Examiner
U. PRIYANKA, M.sc., M.Phil., A.V.C.College (Autonomous) Assistant Professor of Mathematics. Mannampandal.
Mayiladuthurai 609 305.
2020
CERTIFICATE This is to certify that this project work was done under my guidance and the
dissertation entitled " A STUDY ON SUMS OF POWERS OF RECIPROCALS
OF SOME POLYGONAL NUMBERS " submitted by R.DHARANI
(Reg. No. P187832) in partial fulfillment of the requirements for the award of the
Degree of Master of Science in Mathematics during 2018 2020 is the original work of the candidate.
R Signature of the Candidate Signaturedof the Guide
Signature of the Head ofthe PPHRA1Ssc M Phi D. Dr. S. GOV
Head and Associate Professor, Department of Mathematics.
A VC College(AutonomousS) Mamampandal-609 305
Signatuke'of the Examiner
M B VA1, M, M il A VCllege (A utonomrus) Mannapandal Mayiladulluras »
Analt Piofstht M.athemab
2112
CLRT1CATE
) Cly hat t projeut muk was drne under my uinlanca: and thig
dnelati1nCnild "A STUDY (N TKANGOLAR FUZIY MATKICES
uubllcl by
A. DIVYA (R«yNo,P187433)
hartianl lullilment f the requrcment, for thc award of thie: Degroe of Master t
SCe Matlemalics dung 201h-2920. I1 1s the original wsk f the tandidate
1tcandidale Signafure of ie Candidate Signature of the (uide
Dr. S. CovINDARAADatre B1iy Weàad of the Department Heal a r1d Assoriate Profussuf
Department of Mathematics,
AVC rlnge (AIutrafiturnityus) Mannarnpandal 6 09 309
Signataret the Fxaminer
Mrs.B.RADHABHARATHI,M.Sc.,M.Phil.,M. B.A.. A.V.C.COLLEGE(Autonomous)
Mannampandal, Mayiladuthurai 609 305.
Assistant Professor of Mathematics
2020
CERTIFICATE
This is to certify that this project work was done under my guidance and the
dissertation entitled "A STUDY ON CHARACTERIZATION OF FUZZY
SELF CENTERED GRAPHS"submitted by G.GAYATHRI (Reg.No. P187834)
in partial fulfillment of the requirements for the award of the Degree of Master of
Science in Mathematics during 2018-2020. It is the original work of the candidate
oGaalhyi Signature of the Candidate Signature of the Guide
Signature of the Héai óf the Department Dr.S. GOVINDARAJAN.M S.M Pma sÓ
Head and Associate Professor, Department of Mathematics,
AVC Coliege (Autonomous). Mannampandal-609 305.
Signature of tne Examiner
Mrs.A.BANUMATIY,M.sc.. M.Phil.,B.Ed.PGDCA. A.V.C. College(Autonomous)
Assistant Professor of Mathematics, Mannampandal,
Mayiladuthurai-609305. 2020.
CERTIFICATE
This is to certify that this projeet work was done under my guidance and
the dissertation entitled A STUDY ON PROPERTIES OF FUZZY
GRAPH3 submitted by
M. GOWSALYA
(Reg. No. P187835)
In partial fulfillment of the requirements for the award of the Degree of Master
of Science in Mathematics during 2018 -2020. It is the original work of the
candidate.
M.Gu aalo9/na0 Pon 24, J.9
Signature of the Candidate Signature of the Guide
Sigadture of the Signature ofhe Head of the Departmenpni Ph.D., Dr.S. GOVINDARAJAN,MSc.MPhil.Ph.D.
Head and Associate
Protessor,
Department of Mathematics,
A V.C College (Autonoimous),
Mannampandal-609 305.
External Examineer
Mr. V. SlJAN MADHAVAN, M.Sc.,M.Phil., B.Ed., Assistant Professor,
A.V.C. College(Autonomous). Mannampandal-609305.
Mayiladuthurai. 2020.
PG &Research Department of Mathematics
CERTIFICATE
This is to certify that this project work was done under my guidance
and the project entitled "ON VERTEX VALUATIONS OF m-SUPER
SUBDIVIDED GRAPH" submitted by B.INDUMATHI
(Reg.No.P18 7836) in partial fulfilment of the requirements for the award of
the Degree of Master of Science in Mathematics during 2018 -2020 is the
original work of the candidate.
B. indumalth
Signature of the candidate Signature of the Guide
(VSJHN NODINavw
Signature of 'thefiéad of the Department Dr. S. GOVINDARAJAN,MSC.MPhl Ph D Head and Associate Professoi.
Department of Mathematics, AV.C College (Autonomous),
Mannampandal-609 305. 191
Signature of the External Examiner
|pe
Mrs.A.BANUNIATIIY,M.sc., M.Phil.B.Ed.PGDCA.. AssistantProfessor of Mathematics,
A.V.C. College(Autonomous)
Mannampandal. Mayiladuthurai-609305. 2020.
CERTIFICATE
This is to certify that this project work was done under my guidance
and the dissertation entitled DOMINATION IN
FUZZY GRAPHS" submitted by
R. KEERTHANA(Reg.No:P187837)
In partial fulfillment of the requirements for the award of the Degree
of Master of Science in Mathematics during 2018-2020.It is the original
work of the candidate.
orVasar 2afo R Keeitana Signature of the Candidate Signature of the Guide
D..VASANTHT, bail Phd. Asshlant Professor sthei atic,
A.V.C. College (AulSh6HMH Mannam and
Mayiladuthurai- oe S9.
Signatureof tle' Head of the Department Dr. S. GOVINDARAJAN,MSc.M Phil.Ph.D.
Head and Associate Protessor,
Department of MathematiCs
A V.C. College (Autonomous).
Mannampandal-609 305
SignaturebOVhe Examiner
Mr.T.RAGATAN, I.Se..M.Phil.. A.V.C.COLLEGEGAutonomous) Assistan Professor of Mathematies. Department of Mathenaties.
Manmanpandal. Mayiladuthuai 609 305. 2020
CERIIFICATE
his is to cenily tat this project work was done under my guidance and the
dissertation entitled "A STUDY ON WIENER VECTOR, IIYPER-WIENER
VECTOR,WIENER NUMBER,IIYPER-WIENER NUMBER OF GRaPH"
submitted by
M.MONISHA (Reg.No. P187838)
n partal fulfillment of the requirements for the award of the Degree of Master of
Science in Mathematics during 2018-2020. It is the original work of the candidate.
.Menng Signature of the Candidateaalp9hoo0 Signature of the Guide
Sigature uf th�' He�d of thetRepatinlit S P1 Department of Mathematics,
AVC.College (Autonomous).
Mannampandal-609 305.
Signature e Examiner
Dr. B. ARTHI, M.Sc., M.Phil., Ph.D. A.V.C. College (Autonomous),
Assistant Professor, Mannampandal, Department of Mathematies. Mayiladuthurai,2020
CERTIFICATE
This is to certify that the project work was done under my guidance and the
dissertation entitled "A STUDY ON ORTHOGONAL POLYNOMIAL MATRIX"
Submitted by G. NISHANTHI(Reg.No.P187839)
In partial fulfillment of the requirements for the award of the Degree of Master
of Science in Mathematices during 2018-2020 is the original work of the candidate.
B Signature of the candidate Signature or ihe Guide
Signature of the Hesd Df shaMUpIDAMAMN,M SC.MPhil.PhD Head and Associate Protessor,
Department of Mathematics A.V.C. College (Autonomous),
Mannampandal-609 305.
Signatura ofthe External Examiner
Dr. S. MOHAN, M.Se., M.Phil. B.Ed. Ph.D., DCA. A. V. C. College(Autonomous).
Assistant Professor in Mathematics. Mayiladuthurai.
PG and Research Department of Mathematics Mannampandal- 609 305
.9. 2020
CERTIFICATE
This is to certify that this project entitled "A STUDY ON 1-MATRIX AND IT'S
PROPERTIES" was done under my guidance and the dissertation submitted by
A. PAVITHRA (Reg. No. P187840)
In partial fulfillment of the requirements for the award of the Degree of Mlaster of
Science in Mathematics during 2018-2020. It is the original work of the candi date
Aalu Signature of the Candidate
(A. Pavithra)
Signature of the Guide (Dr. S. Mohan)
Signatiesfthe Head of the Depurtment Signatureef the External Examiner
Dr.S. GOVINDARAJAN,M
Sc.MPhil. Ph D.
Head and Associate
Professor,
Department of Mathematics
AVC College (Autonomous) Mannampandal 609 305.
Dr. L.ASANTUI M.S., M.Phil.. Ph.). A.NCCOLLEGE. (Autonomous) Mannaandal. Mayiladuthura 609 305.
AssIstant P'rotessor in Mathenmaties.
2020
CERTIFCATE
This is t0 certity that this projeet work was done under my guidance and
the dissertation entitled " A STUDY ON CATALAN NUMBERS'submitted by
K.POOJA
(Reg.No. Pi87841)
in partial fulfillment of the requirements for the award of the Degree of Master of
Seience in Mathematies during 2018 - 2020. It is the original work of the
candidate.
Vason Signature of the R. Signature of the Candidate Dr. L. VASANTHI,M.Sc M Phil.PhD Assistant Professor of Mathematics,
A.V.C. College (Autonomous) Mannampandal,
Mayiladuthurai. 609 305
Signature olthè lHead of the DepartaeatDARAJAN.MSC.M P. PhD.
Head and Associate
Protessor,
Department of Mathematics,
A VC College (Autonnmous).
Mannampandal 609 305
Signature fthe Examiner
Mr. V.SIJAN MADILAVAN, M.Se.. M.Phil.. B.Ed., A.V.C. College (Autonomous).
Assistant prolessor Mannampandal-609305 PG &Rescarch Department of Mathematics Mayiladuthurai.
2020
CERTIFICATE
This is to certify that this project work was done under my guidance
and the project entitled "ON ODD ,ODD-EVEN GRACEFULNESS OF
SOME WELL KNOWN GRAPHS" submitted by P.A.RAKSHA
(Reg. No: P18 7842) in partial fulfillment of the requirements for the
award of the Degree Of Master Of Science In Mathematics during 2018-
2020 is the original work of the candidate.
Pa Pelu Signature of the Candidate Signature of the Guide
(VSIJAN MADHAVAN)
Dr.S. GOVINDAR re Had of the Department Head and Associate Protessor Department of Mathematics
A.V.C. College (Autonomous), Mannampandal-609 305. 2
Signature ofthe External Examiner
MRS.B.REVATHI,M.Sc.M.Phil. Assistant Prolessor of Mathematics.
A.V.C.COLLEGE(AUTONOMOUS) Mannampandal Mayiladuthurai 609 305.
2020
CERTIFICATE
This is to certily that this project work was done under my guidance and the
dissertation entitled "A STUDY ON SECONDARY K-NORMAL MATRICES"
submitted by A.RAMYA (Reg.No. PI87843) in partial fulfillment of the requirements
tor the award of the Degree of Master of Science in Mathematics during 2018- 2020. It
is the original work of the candidate.
Signature of the Candidate Signafure of the Guide
Signature ofthewad of the Department
Dr.S. GOVINDARAAN,M Sc.MPhil.Ph.D. Head and. Associate Professor, Department of Mathematics.
A VC. College (Autonomous) Mannampandal-609.305
Signatureffhe Ëxaminer
Dr.S. MOHAN, MSe.. N Phil. BEd, Ph.D., DCA AV.C College(Autonomous). Assistant Protessor in Mathematics. Mayiladuthurai,
PG and Research Department of Mathematics Mannampandal-609 305.
24 .2020.
CERTIFICATE
This is to certity that this project entitled "A STUDY ON J-MATRIX AND IT'S
RELATED CONCEPTS" was done under my guidance and the dissertation submitted
P. SATHYA (Reg. No. P187844)
In partial fulfillment of the requirements for the award of the Degree of Master of
Science in Mathematics during 2018 -2020. It is the original work of the candidate.
P Sathya Signature of the' Candidate Signature of the Guide
(P. sathya) (Dr. S. Mohan)
Signature f thATeud of the Department Signature of the External Examiner
ss OCte utoss0'
f atherTfcs
Mrs.K.SINDHU, M.Sc., M.Phil., A.V.C.COLLEGE Assistant Professor of Mathematics (Autonomous)
Mannampandal, Mayiladuthurai - 609 305
2020.
CERTIFICATE
This is to certify that this project work was done under my guidance and the
dissertation entitled "A STUDY ON CHANGING AND UNCHANGING
DOMINATION NUMBER OF A ZERO-DIVISOR GRAPH" submitted by K. SHAILAJA (Reg. No. P187845) in partial fulfillment of the requirements for
the award of the Degree of Master in Mathematics during 2018 2020. It is the
original work of the candidate.
K.Shaiaja Signature of the Candidate igna od Signatüreqf the Guide
Signature of the H ad' of the Department Dr.S. GOVINDARAJAN,MSC.M.Ph P
Head and Associate Profes Department of Mathematics
A.VC. College (Autonomous Mannampandal-609 305.
Signature of ih täaminer
Dr. L.V ASANTHI, M.Sc., M.Phil., Ph.D. A.V.C.COLLEGE, (Autonomous)
Mannampandal. Mayiladuthurai
ssistant Professor in Mathematics, 609 305.
2020
CERTIFICATE
This is to certity that this project work was done under my guidance and
the dissertation entitled "A STUDY ON LINE GRAPHS AND QUASI
TOTAL GRAPHS" submitted by
S.SUGANYA
(Reg.No. P1878465)
in partial fulfillment of the requirements for the award of the Degree of Master of
Science i Mathematies during 2018 2020. It is the original work of the
candidate.
S Sugarya Signature of the Candidate Signature ABNYAe Dr.L
Assisiani Protessur t ne ntrs.
A.V.C. Coliege (Autenomous)
Mannampandal Mayiladuthurai 609 305.
SignarureSf the Head of the RepamnRhte Protesu Head
and Associate
Protessor,
DepartIent of Mathematic:s
AVC College (Autonomous)
Mannampandal-609 305.
Signature KrAhe Examiner
Dr.R.MANIKANDAN, IS. IPhil. A.V.C.COLLEGE(Autonomous)
BEd., MIBA., Ph.D. Mannampandal.
Assistant Professor of Mathematics Mayiladuthurai 609 305.
21.09.2020
CERTIFICATE
This is to certily that this project work was done under my guidance and
the dissertation entitled "A STUDY ON QUASI QUATERNION NORMAL
MATRIX" submitted by
M. YOGALAKSIMI (Reg.No. P187847)
In partial fullillment of the requirements for the award of the Degree of
Master of Science in Mathematics during 2018- 2020. It is the original work of the
candidate.
M-yo ) q Jathwni Signature of the Candidate 2ela Signature of the Guide2
o
Signature of the Hehndf the Department Dr.S. GOVINDARAJAN,M.Sc,MPhil.Ph.D,
Head and Associate Professor Department of Mathematics,
A.V.C. College IAutonomous),
Mannampandal-609 305
Signatureto kkaminer
Mrs.S. AARTIY, M Se.,MPlhil. . AV
AssIstant P'rolessO Mathemati (Auo
M andal
Mayillutha ,)
CLRIL1CALL This 1s to ceituly thal th projeet wo wia done undermy udane n dseil,ti
entitled "A STUDY ON DETNORM UZZY MATRIX" ullted y PPAVITHA (Reg.No. PI87848) m partial ulfillmet of the 1quem"nlor tr awdol the Dezree l Ma:.ler of Science in Matlhematics durng 201R 2)20 I e oInal wk l the andidate
P:Pavilhrna Signature of the Candidate ure the (.uidMo}o
signature ofhe ieza r the Department Dr. S. GOVINDARAJAN "PD
Head and AssoCiate Pr)t!isor Departnent of MathematiCs
AVC College IAutononous) Mannampandal 609 305
Signaturef he Examiner
MrsA.BANUMATIIY, M.se., M.Phil., B.Ed.. PGDCA. A.V.C. CollegetAutonomous)
Assistant Professor in Mathematics Maampandal.
Mayiladuthurar 609 305.
24.9.2020.
CERTIFICATE This is to certify that this project work was done under my guidance and the
dissertation entitled "TSOLUTION OF FUZZY TRANSPORTATION
PROBLEM USING FUZZY LINEAR SYSTEM" submitted by
A.PADMA PRIYA (Reg.No:P187849)
In partial fulfillment of the requirements for the award of the Degree of Master of
Science in Mathematics during 2018-2020. It is the original work of the candidate.
A.l
Signature of the Candidate Signature of the Guide
Signature o tié Tlead of the Department
19p
Signature bf the Examiner
Dr.S.GOVINDARAJAN,MSc.MPhil.Ph.D Head and Associate Professor
Department of Mathematics. A VC. College (Autonomous),
Mannampandal-609 305.
Mrs.B.REVATHI, M.Sc., M. Phil., Assistant professor of mathematics,
A.V.C.COLLEGE(Autonomous) Mannampandal, Mayiladuthurai-609 305,
2020
CERTIFICATE
This is to certify that this project work was done under my guidance and the
dissertation entitled "A STUDY ON FUZZY LoGICAL PROPOSITIONS" submitted by
R.KARPAKAM(Reg.No.P187850)
In partial fulfillment of the requirements for the award of the Degree of Master
of Science in Mathematics during 2018-2020. It is the original work of the
candidate.
Rpakam Siguaturé of Candidate Signature of the Guide
Signature of t lead of the Department
Dr S. GOVINDARAJAN,M
Sc 1 Phii PhbD,
Head and AssOCiale
Professor,.
Department of Matheinatics,
A V.C.College (Aulonomous)
Mannampandal 609 305
Signature of the Examiner
Mrs. K. SINDHU, M.Sc., M.Phil., A.V.C COLLEGE(Autonomous)
Assistant Professor of Mathematics Mannampandal, Mayiladuthurai -609 305.
2020.
CERTIEICATE
This is to certify that this project work was done under my guidance and the
dissertation entitled "A STUDY ON S-NORMAL MATRICES" submitted by
D.RENIDA MARY (Reg. No. P187851)
In partial fulfillment of the requirements for the award of the Degree of Master of
Science in Mathematics during 2018-2020. It is the original work of the candidate.
. Signature of the Guide
Signature of the Candidate
191o
Signature of the lIeayf the Department Dr. S. GOVINDARAJAN,MSc.M.Phil.Ph.D,
Head and Associate
Professor,
Department of Mathematics,
A.V.C. College (Autonomous),.
Mannampandal-609 305.
Signature of the Examiner
Dr. R.MANIKANDAN, M.sc, M.Phil., B.Ed., MBA., Ph.D., A.V.C.COLLEGE(Autonomous),
Assistant Professor of Mathematics, Mannampandal, Mayiladutlhurai, 609 305
2020
CERTIFICATE
This is to certify that this project work was donc under my guidance and
the dissertation entitled "A STUDY ON HADAMARD MATRIX" submittcd
by P. GEETHA (Reg. No. P187852) in partial fulfillment of the reyuirements
for the award of the Degrce of Master of Science in Mathematics during 2018-
2020. It is the original work of the candidate.
P hedha Signature of the Candidate Signature of the Guide
Signature of the efthe Department GOV*NDARAJAN,M.Sc.,M.Phil.Ph.D, Head and Associate Professor,
Department of Mathematics, A.V.C. College (Autonomous).
Mannampandal-609 305.
Signature Examiner
Mrs.B.RADHABHARATHI,M.Se.M.Phil.,M.B.., A.V.C.COLLEGE(Autonomous) Assistant Professor of Mathematics Mannampandal,
Mayiladuthurai - 609 305.
2020.
CERTIFICATE
This is to certify that this project work was done under my guidance and the dissertation
entitled"A STUDY ON MAXx-PLUS ALGEBRA AND APPLICATION TO
MATRIX OPERATIONS submitted bys. SRIPRIYA (Reg. No. P187853) in partial
fulfillment of the requirements for the award of the Degree of Master of Science in
Mathematics during 2018-2020. It is the original work of the candidate.
B.2 Signature of the Guide Signature of the Candidate
Signature df thienaaad of the Department
Dr.S.GOVINDARAJAN,M Sc.M.Phil.Ph.D Head and Associate Professor, Department of Mathematics, A.V.C. College (Autonomous).
Mannampandal-609 305.
Signaturetyhe Examiner
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