On Edge-Hamiltonian Property of Cayley Graphs

Abstract

Let G be a group generated by X. A Cayley graph over G is defined as a graph G(X) whose vertex set is G and whose edge set consists of all unordered pairs [a,b] with a, b ε{lunate} G and a-1b ε{lunate} X ∩ X-1, where X-1 denotes the set {x-1 {divides} x ε{lunate} X}. When X is a minimal generating set or each element of X is of even order, it can be shown that G(X) is Hamiltonian if it is edge-Hamiltonian. Hence every Cayley graph of order a power of 2 is edge-Hamiltonian. © 1988.