CERTIFICATE - AVC College

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),


Signature of the Exter^al EKaminer

DI$.AWINDARAJANRS MP.D

Hes1 na Associate

Protessor,

Departrent of Mathematics,

A.VC. College (Autenomous),


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.


Department of Mathematics, A.V.C. College (Autonomous),


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,


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,


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.



A.V.C. Coliege (Autonomous).


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


A V.C College (Autonomous).


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,


A.V.C. College (Autonomouss).


Signature of the External Examiner

Dr.S. SENTHILKUMAR, M Sc.M Phil,Fh.D AssistaHr Professor in Mathema ic PG Department of Mathematcs,


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.,


Department of Mathematics, A.V.C. College (Autenomous).


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


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,


A.V.C. College (Autonomous), Mannampandal-609 305.


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,


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


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


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


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.


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


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.


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


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


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


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


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


Sigadture of the Signature ofhe Head of the Departmenpni Ph.D., Dr.S. GOVINDARAJAN,MSc.MPhil.Ph.D.

Head and Associate

Protessor,


A V.C College (Autonoimous),


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


|pe

Mrs.A.BANUNIATIIY,M.sc., M.Phil.B.Ed.PGDCA.. AssistantProfessor of Mathematics,

A.V.C. College(Autonomous)

Mannampandal. Mayiladuthurai-609305. 2020.

CERTIFICATE


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).


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).


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)


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),


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)


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,


A VC College (Autonnmous).


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


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-


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)


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


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)


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)


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),


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.


dissertation entitled "TSOLUTION OF FUZZY TRANSPORTATION

PROBLEM USING FUZZY LINEAR SYSTEM" submitted by

A.PADMA PRIYA (Reg.No:P187849)



A.l


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),


Mrs.B.REVATHI, M.Sc., M. Phil., Assistant professor of mathematics,

A.V.C.COLLEGE(Autonomous) Mannampandal, Mayiladuthurai-609 305,

2020

CERTIFICATE


dissertation entitled "A STUDY ON FUZZY LoGICAL PROPOSITIONS" submitted by

R.KARPAKAM(Reg.No.P187850)


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)


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


dissertation entitled "A STUDY ON S-NORMAL MATRICES" submitted by

D.RENIDA MARY (Reg. No. P187851)



. 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,


A.V.C. College (Autonomous),.


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).


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).


Signaturetyhe Examiner

CERTIFICATE - AVC College

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