پديد آورنده :
چناري، مريم
عنوان :
گراف هاي كيلي جمعي و كيلي جذبي
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
[هفت]، ۷۱ص.: مصور
استاد راهنما :
بيژن طائري
استاد مشاور :
محمدرضا ودادي
واژه نامه :
فارسي به انگليسي
توصيفگر ها :
گراف كيلي , گراف كيلي جمعي , گراف كيلي جمعي يكاني , گراف كيلي جذبي , كمر , گراف مسطح
استاد داور :
عليرضا عبداللهي، محمود بهبودي
تاريخ ورود اطلاعات :
1397/04/27
چكيده انگليسي :
Addition Cayley graphs and absorption Cayley graphs Maryam Chenari m chenari@math iut ac ir June 13 2018 M Sc Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Bijan Taeri Professor b taeri@cc iut ac irAdvisor Mohammad Reza Vedadi Associate Professor mrvedadi@cc iut ac ir2000 MSC 20K01 05C25 05C50 05C45 15A18 Keywords Cayley graph absorption Cayley graph addition Cayley graph planar graph diameter girth Abstract This M S c thesis is based on the following papers Sinha D and Sharma D absorption Cayley graph Electronic Notes in Discrete Mathemetics 53 2016 395 412 Sinha D Garg P and Singh A Some properties of unitary addition Cayley graphs NNTDM 17 3 2011 49 59 Let G be a finite group and S be a subset of G such that S S 1 and 1G S Then Cayley graph denoted by Cay G S with respect to S is a graph with vertex set G and edge set E G S gh hg 1 S It is easy tosee that Cay G S is S regular A special kind of Cayley graph is the unitary Cayley graph of additive group Zn where n is a positive integer with respect to S Un the set of units of Zn Thus the vertex set of Cay Zn Un is Zn and there is an edge between two vertices x y if and only if x y is a unit in Zn For a subset S of an abelian group G the addition Cayley graph denoted by Cay G S is a graph with the vertexset G and the edge set g1 g2 g1 g2 S The unitary addition Cayley graph Cay Zn Un is a specialkind of addition Cayley graph We say that an element 1 b Zn absorbed in a Zn if ab a We say that a is an absorption element ofZn Let S be the set of all absorption elements of Zn that is S a Zn ab a for some b Zn b a b 1 The addition Cayley graph with respect to S denoted Zn is called the absorption Cayley graph In this thesis we review some of the basic definitions and standard terminology of graph theory number theory group theory and additive combinatoricse respectively We study basic properties of Cayley graph addition Cayleygraph unitary Cayley graph and unitary addition Cayley graph respectively We show that the Cay Zn Un isisomorphic to the Cay Zn Un if and only if n is even We show that Cay G S is complete if and only if eitherS G or S G 0 and G is an elementary abelian 2 group Also we study the connectedness hamiltoniacity planarity girth of the absorption Cayley graph Zn We show that the absorption Cayley graph Zn cannotbe Eulerian Also we show that the Zn is the complement of unitary addition graphs if n 2m m is odd andit is bipartite if and only if n p where p is prime We show that an absorption graph Zn is connected if and only if n p 1 p 2 pk k where pi pj for i j pi is prime and k 2 12
استاد راهنما :
بيژن طائري
استاد مشاور :
محمدرضا ودادي
استاد داور :
عليرضا عبداللهي، محمود بهبودي
