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PROJECT DETAILS - Department of Mathematics (Sf) - III UG PROJECT DETAILS - Department of Mathematics (sf) - III UG Name of the Guide with S.No Reg.No Name of the Student Department Title of the Project designation 1 15BM4423 K.N. Abiyurekha B.Sc Mathematics (SF) 2 15BM4429 S. Divya B.Sc Mathematics (SF) Dr. Mrs. A. Anis Fathima, Bellman Ford Algorithm in 3 15BM4431 K. Jaya Alamelu B.Sc Mathematics (SF) M.Sc., M.Phil., PGDCA., Graph Theory 4 15BM4456 J. Powmiya B.Sc Mathematics (SF) Ph.D., 5 15BM4464 R. Sumithra B.Sc Mathematics (SF) 6 15BM4445 P. Manimekalai B.Sc Mathematics (SF) 7 15BM4446 B. Muthukavitha B.Sc Mathematics (SF) Dr. Mrs. A. Anis Fathima, Ford Fulkerson Algorithm in 8 15BM4451 G. Naveena B.Sc Mathematics (SF) M.Sc., M.Phil., PGDCA., Graph Theory 9 15BM4453 S. Pavithra(15/7/98) B.Sc Mathematics (SF) Ph.D., 10 15BM4462 R. Sneha B.Sc Mathematics (SF) 11 15BM4426 D. Baby sudha B.Sc Mathematics (SF) 12 15BM4428 A. Devipriya B.Sc Mathematics (SF) Distance Regular and Distance Ms.J.Priyadharshini,M.Sc.,M. 13 15BM4435 S. Karthika B.Sc Mathematics (SF) Transitive Graphs in Graph Phil., 14 15BM4444 G. Maheshwari B.Sc Mathematics (SF) Theory 15 15BM4460 M. Santhiya B.Sc Mathematics (SF) 16 15BM4422 S. Abinaya B.Sc Mathematics (SF) 17 15BM4427 T. Chellam Rajalakshmi B.Sc Mathematics (SF) Vector Calculs in three Ms.J.Priyadharshini,M.Sc.,M. 18 15BM4436 K. Kavibharathi B.Sc Mathematics (SF) dimensional space Phil., 19 15BM4450 S. Nandhini B.Sc Mathematics (SF) 20 15BM4468 J. Vinothini B.Sc Mathematics (SF) 21 15BM4425 B. Aruthra B.Sc Mathematics (SF) 22 15BM4430 G. Ishwarya B.Sc Mathematics (SF) An application of metric space Mrs. A. Samsath, 23 15BM4434 K. Kalaivani B.Sc Mathematics (SF) and metric dimension in Graph M.Sc.,M.Phil., 24 15BM4438 R. Kaviyapriya B.Sc Mathematics (SF) theory 25 15BM4465 C. Surya Prabha B.Sc Mathematics (SF) 26 15BM4424 V. Arokiya Sundhari B.Sc Mathematics (SF) 27 15BM4439 C. Keerthana B.Sc Mathematics (SF) Distance in Graph theory and Mrs. A. Samsath, 28 15BM4440 S. Keerthana B.Sc Mathematics (SF) its application M.Sc.,M.Phil., 29 15BM4442 G. Kiruthikadevi B.Sc Mathematics (SF) 30 15BM4457 S. Powranika B.Sc Mathematics (SF) 31 15BM4437 M. Kaviya B.Sc Mathematics (SF) 32 15BM4447 M. Muthulakshmi B.Sc Mathematics (SF) 33 15BM4455 R. Pavithra B.Sc Mathematics (SF) Cordial Labelling of Degree Mrs. T. Vanjikkodi, M.Sc., 34 15BM4458 P. Rajeswari B.Sc Mathematics (SF) Splitting graphs M.Phil., PGDCA 35 15BM4463 R. Sugathakumari B.Sc Mathematics (SF) 36 15BM4466 P.Swathi B.Sc Mathematics (SF) 37 15BM4433 S. Kalaiselvi B.Sc Mathematics (SF) 38 15BM4443 M. Kousalya B.Sc Mathematics (SF) 39 15BM4449 K. Nandhini B.Sc Mathematics (SF) Path Optimization Algorithm Ms. G. Dhivya, M.Sc., 40 15BM4452 P. Nithya Priya B.Sc Mathematics (SF) and Dijkstra’s Algorithm M.Phil., 41 15BM4454 S. Pavithra(2/6) B.Sc Mathematics (SF) 42 15BM4459 G. Saidharani B.Sc Mathematics (SF) 43 15BM4432 J. Jeyapritha B.Sc Mathematics (SF) Graphical and Queuing Model 44 15BM4441 K. Kiruthika B.Sc Mathematics (SF) of Banking Operations in Ms. J.P. Thempaavai, M.Sc., 45 15BM4448 K. Nandhika B.Sc Mathematics (SF) Intercontinental Bank Plc, M.Phil., 46 15BM4461 G. Sarumathi B.Sc Mathematics (SF) Nigeria 47 15BM4469 K. Vishnu Priya B.Sc Mathematics (SF) DISTANCE TRANSITIVE AND DISTANCE REGULAR GRAPHS IN GRAPH THEORY A Group Project Report Submitted in partial fulfilment of the requirement for the award of the degree of Bachelor of Science in Mathematics Submitted by D. BABY SUDHA (15BM4426) A. DEVIPRIYA (15BM4428) S. KARTHIKA (15BM4434) G. MAHESHWARI (15BM4444) M. SANTHIYA (15BM4459) Under the guidance of Ms. J. PRIYADHARSHINI M.Sc., M.Phil., Assistant Professor Department of Mathematics Sri G.V.G Visalakshi College for Women (Autonomous) (Affiliated to Bharathiar University, Coimbatore) Re-Accredited at ‘A’ Grade by NAAC (CGPA 3.53) An ISO 9001:2008 Certified Institution Udumalpet – 642 128 October – 2017 CERTIFICATE This is to certify that the Group Project work entitled “DISTANCE TRANSITIVE AND DISTANCE REGULAR GRAPHS IN GRAPH THEORY” is a bonafied record work done by Group members D.Baby sudha(15BM4426), A. Devipriya(15BM4428), S.Karthika (15BM4434), G.Maheshwari (15BM4444), M.Santhiya (15BM4459) submitted in Partial fulfilment of the requirements for the award of the degree of Bachelor of Science in Mathematics at Sri G.V.G Visalakshi College for Women (Autonomous), Udumalpet during the academic year 2015-2018. Submitted for the Viva- voce held on ____________. Signature of the Guide Signature of the H.O.D Internal Examiner External Examiner DECLARATION We hereby declare that the project entitled “DISTANCE TRANSITIVE AND DISTANCE REGULAR GRAPHS IN GRAPH THEORY”submitted in partial fulfilment of the requirements for the award of the degree of Bachelor of Science in Mathematics is a record of original project done by us during the period of study in Sri G.V.G Visalakshi College for Women (Autonomous) Udumalpet, under the supervision and guidance ofMs. J. Priyadharshini M.Sc., M.Phil., Assistant Professor, Department of Mathematics. Place: Udumalpet Signature of the Candidates, Date: ACKNOWLEDGEMENT First and foremost, we record our sincere gratitude to the Almighty for her blessings for the successful completion of the project. We take immense pleasure in expressing our thanks to the management for their continuous support throughout the project. We are extremely grateful to the Principal Dr.(Mrs.) K. Punithavalli M.Com., M.Phil., PGDCA.,Ph.D., Sri G.V.G Visalakshi College for Women (Autonomous) for providing all the facilities to do this project. We take privilege in expressing our sincere, heartfelt thanks and gratitude to Dr. (Mrs) A. AnisFathima M.Sc., M.Phil., PGDCA., Ph.D., Head and Assistant Professor , Department of Mathematics for her continuous support throughout the project. We record our profound sense of indebtness to our guide Ms.J.Priyadharshini M.Sc., M.Phil., for taking a keen interest and given us valuable suggestions, guidance in all aspects of this group project. We express our deep gratitude and humble thanks to the faculty members of the department for their valuable suggestions and lending helping hand for the successful completion of our group project. Finally we would like to thank our parents and Friends who have contributed much to complete the group project work on time. D. BABY SUDHA (15BM4426) A. DEVIPRIYA (15BM4428) S.KARTHIKA (15BM4434) G. MAHESHWARI (15BM4444) M.SANTHIYA (15BM459) CONTENT TITILE ABSTRACT INTRODUCTION CHAPTER -1 [DISTANCE TRANSITIVE] CHAPTER -2 [DISTANCE REGULAR ] CHAPTER -3 [TYPES OF DISTANCE TRANSITIVE] CHAPTER -4 [PRIMITIVE & IMPRIMITIVE GRAPHS] CONCLUSION BIBILOGRAPHY ABSTRACT Graph theory is a study of graphs, which are mathematical structures used to get model pairwise relation between objects. In this we will discuss about the distance transitive graphs and distance regular graphs. In this project, we discuss about the connectivity of distance transitive to the concept of vertex transitive and distance. And we will also define the distance partition and Intersection array to show a graph is distance regular. We connect the concept of distance transitive graphs to explain the three different types of distance transitive graphs. We also study the concept of the distance transitive to know about the primitive and imprimitive graphs. INTRODUCTION In this paper, we will discuss about the distance regular graph and the intersection algebra for these graphs which is based upon its intersection numbers. Distance-transitive graphs were first defined by Norman L. Biggs and D.H. Smith in1971. In the Mathematical field of graph theory, a distance-transitive graph is a graph such that given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance i, then there is an automorphism of the graph that carries v to x and w to y. Every distance-transitive graph is distance- regular but the converse does not necessarily hold, as first shown by Adel'son-Vel'skiietal. PRELIMINARIES: GRAPH: A graph is a diagram consists of points called vertices, joined by lines called edges each edge join exactly two vertices. PATH: A path is a walk in which all the edges and all the vertices are different. ISOMORPHISM: Two digraphs C and D are isomorphic if the graph D can be obtain by relabeling the vertices of C that is, if there is one to one correspondence between the vertices of C and those of D, such that the arcs joining each pair of vertices in C agree both number and direction with the arcs joining the corresponding pair of vertices in D. ADJACENT: The vertices v and w of the diagram are adjacent vertices if they are joined (in either direction) by an arc e. u w REGULAR GRAPH: A graph is regular if it vertices all have the same degree. STRONGLY REGULAR GRAPH If a graph G has an intersection array, we say G is distance- regular. If a distance- regular graph has diameter 2, then it is a strongly-regular graph. CONGRUENCE A G- congruence is an equivalence relation≡ on X which is preserved under the action of G, that is x ≡ y <=> g(x)≡g(y) for all g G. For any action we always have the following∈ two G- congruence The trivial G- congruence where x≡y <=>x=y; The universal G- congruence where x≡y for all x,y X. ∈ SYMMETRIC A graph is Vertex Transitive if every vertex can be mapped to any other vertex by some automorphism that is it is symmetric. DIAMETER In a graph G, the greatest path between two vertices is called as the diameter of the graph G.
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