Finite 1-Regular Cayley Graphs of Valency 5. (27th March 2013)

• Record Type: Journal Article
• Authors: Li, Jing Jian; Lou, Ben Gong; Zhang, Xiao Jun
• Other Names: Li Cai Heng Academic Editor.
• Is Part Of: International journal of combinatorics. Volume 2013(2013)
• Publication Date: 2013-03-27
• Subjects: Combinatorial analysis -- Periodicals; Combinatorial analysis; Periodicals; Electronic journals; 511.605
• DOI: 10.1155/2013/125916
• Languages: English
• ISSNs: 1687-9163

Abstract

Abstract : LetΓ = C a y ( G, S ) andG ≤ X ≤ A u t Γ . We sayΓ is( X, 1 ) -regular Cayley graph ifX acts regularly on its arcs.Γ is said to be core-free ifG is core-free in someX ≤ A u t ( C a y ( G, S ) ) . In this paper, we prove that if an( X, 1 ) -regular Cayley graph of valency5 is not normal or binormal, then it is the normal cover of one of two core-free ones up to isomorphism. In particular, there are no core-free1 -regular Cayley graphs of valency5 .