پديد آورنده :
عديلي پور، محسن
عنوان :
همبندي گراف هاي كيلي جمعي
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
علوم رياضي - رياضي محض
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
بيژن طائري
توصيفگر ها :
همبندي راسي گراف , زوج مقدماتي , شرط كمپرمن
تاريخ نمايه سازي :
21/10/93
استاد داور :
عليرضا عبدالهي، محمدرضا ودادي
چكيده انگليسي :
Connectivity of addition Cayley graphs MOHSEN ADILIPOUR m adilipour@math iut ac ir September 22 2014 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Bijan Taeri b taeri@cc iut ac irAdvisor Mr Mohammad Mashkouri mohammad@cc iut ac ir2000 MSC 05C25 05E18 20F99 Keywords Addition Cayley graph Vertex connectivity of graph Elementary pair Kemperman s conditionAbstract This M Sc thesis is based on the following paperDavid Grynkiewicz Vsevolod F Lev Oriol Serra Connectivity of addition Cayley graphs Journalof Combinatorial Theory Series B 99 2009 202 217 Let S be a subset of an abelian group G The addition Cayley graph of G induced by S which is denoted byCay S is an undirected graph with vertex set G and two vertices g1 g2 G are joined by an edge if and only if Gg1 g2 S Note that if S is finite then Cay S is regular of degree S we assume that each loop contributes G1 to the degree of the corresponding vertex We study some basic properties of addition Cayley graph and showthat Cay S is connected if and only if S is not contained in a coset of a proper subgroup of G with the possible Gexception of the non zero coset of a subgroup of index 2 Let be a graph on the finite set V The vertex connectivity of denoted by is the smallest number ofvertices which are to be removed from V so that the resulting graph is either disconnected or has only one vertex For subsets A and B of an abelian group we write A B a b a A b B Suppose that H is asubgroup of an abelian group G and g G such that 2g S H If set 2 G 2g g G then existenceof g G with 2g S H is equivalent to the condition S 2 G H We put HG S H G S 2 G H S H G and G S min S H H H HG S Then we show that Cay S G S GNow suppose that the subgroups L G0 and G0 G and the element g0 G0 satisfy 1 G0 L is even and larger than 2 G0 g0 L 2 S L GWe define LG S to be the family of all those subgroups L G0 for which a subgroup G0 G lying above L and an element g0 G0 can be found so that properties 1 and 2 hold Setting G S min S L L L LG S and we show that Cay S G S Base on above results we obtain that If S is a proper subset of a finite Gabelian group G then Cay S min G S G S S G
استاد راهنما :
بيژن طائري
استاد داور :
عليرضا عبدالهي، محمدرضا ودادي
