Uniquely shift-transitive graphs of valency 5
Mohammad Iranmanesh, Sh. Sharifi · Filomat · 2018
An automorphism ? of a finite simple graph ? is a shift, if for every vertex v ? V(?),?v is adjacent to v in ?. The graph ? is shift-transitive, if for every pair of vertices u,v ? V(?) there exists a sequence of shifts ?1, ?2,...,?k 2 Aut(?) such that ?1?2...?ku = v. If, in addition, for every pair of adjacent vertices u,v ? V(?) there exists exactly one shift ? ? Aut(?) sending u to v, then ? is uniquely shift-transitive. The purpose of this paper is to prove that, if ? is a uniquely shift-transitive graph of valency 5 and S? is the set of shifts of ? then ?S??, the subgroup generated by S? is an Abelian regular subgroup of Aut(?).