پديد آورنده :
سابقي نژاد، محمد
عنوان :
گراف هاي دوكيلي تك جورساز روي گروه هاي آبلي
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي محض﴿جبر﴾
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
هشت،108ص.: مصور.
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
بيژن طائري
استاد مشاور :
محمد مشكوري
توصيفگر ها :
عمل منظم و نيمه منظم , گراف مشتق , گراف ولتاژ , نگاشت پوشش منظم , گراف كيلي
تاريخ نمايه سازي :
8/11/92
استاد داور :
محمدرضا ريسمان چيان، قهرمان طاهريان
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Abstract This M Sc thesis is based on the following paper Istvan Kovacs Aleksander Malnic Dragan Marusic Stefko Miklavic One matcching bi Cayley graphs over abelian groups European Journal of Combinatorics 30 2009 602 616 Let be a group and be a subset of such that where is the identity element of The Cayley digraph over with respect to is a graph with vertex set and edge set 1 If 1 then is an undirected graph and it is called a Cayley graph Let be subsets of a group such that 1 1 and Define the undirected graph to have vertex set 0 1 and with vertices adjacent if and only if one of the following thre possibilities occurs 1 0 and 1 2 1 and 1 3 0 1 and 1 The graph is called a bi Cayley graph Equivalently a bi Cayley graph may be defined as a graph which admits an automorphism group acting semiregular on the vertex set with two orbits of equal size and is a one matching bi Cayley graph if the bipartite graph induced by the edges joining these two orbits is a perfect matching Typical examples of such graphs are the generalized Petersen graphs The aim of this thesis is to study a classification of connected arc transitive one matching bi Cayley graphs over abelian groups This is done without referring to the classification of finite simple groups Instead complex irreducible characters of abelian groups are used extensively Let be a connected one matching bi Cayley graph over an abelian group This classification can be stated as follows if is arc transitive then it is isomorphic to 0 where one of the following possibilities occurs 1 1 where is one of the following seven orderd paris 4 10 5 2 8 3 10 2 10 3 12 5 24 5 In this case is the unique arc transitive cubic graph 10 2 1 0 1 0 3 1 3 1 In this case is the unique arc transitive cubic graph on 40 points
استاد راهنما :
بيژن طائري
استاد مشاور :
محمد مشكوري
استاد داور :
محمدرضا ريسمان چيان، قهرمان طاهريان
