tailieunhanh - Báo cáo toán học: "Cayley Graphs of Abelian Groups Which Are Not Normal Edge-Transitive"

Đối với một nhóm G, và một tập hợp con S của G 1G ∈ S, chúng ta hãy Γ = Cay (G, S) là đồ thị Cayley tương ứng. Sau đó, Γ được cho là bình thường cạnh bắc cầu, nếu NAut (Γ) (G) là transitive trên mép. Trong bài báo này chúng tôi xác định tất cả các kết nối, vô hướng. | Vietnam Journal of Mathematics 33 3 2005 309-318 V Í e It ini ai m J o mt r im ai I of MATHEMATICS VAST 2005 Cayley Graphs of Abelian Groups Which Are Not Normal Edge-Transitive Mehdi Alaeiyan Hamid Tavallaee and Ali A. Talebi Department of Mathematics Iran University of Science and Technology Narmak Tehran 16844 Iran Received April 15 2004 Revised July 4 2005 Abstract. For a group and a subset of such that . let. be the corresponding Cayley graph. Then is said to be normal edge transitive if . is transitive on edges. In this paper we determine all connected undirected edge-transitive Cayley graphs of finite abelian groups with valency at most five which are not normal edge transitive. This is a partial answer to a question of Praeger. 1. Introduction 310 Mehdi Alaeiyan Hamid Tavallaee and Ali A. Talebi Example . . Theorem . Let be an abelian group and let be a subset of not containing the identity element . . a connected undirected Cayley graph of relative to is an edge-transitive Cayley graph and is not normal edge-transitive as an undirected graph then satisfy one . . . . the cube. Cayley Graphs of Abelian Groups Which Are Not Normal Edge-Transitive 311 the 4-dimensional cube. and m is odd Corollary . All edge transitive connected Cayley graphs with valency at most of a finite abelian group of odd order are normal edge-transitive. All edge-transitive connected Cayley graph with valency at most of a finite cyclic group are normal edge-transitive except for . and . or . and . or . and . or . and . 2. Primary Analysis Proposition . a Cayley graph of group relative on . .contains the right regular permutation of so is vertex- transitive. is connected if and only if. is undirected if and only if