On endo-Cayley digraphs: The hamiltonian property

Given a finite abelian group A, a subset ⊆ A and an endomorphism of A, the endo-Cayley digraph GA( , ) is defined by taking A as the vertex set and making every vertex x adjacent to the vertices (x)+ a with a ∈ . When A is cyclic and the set is of the form = {e, e + h, . . . , e + (d − 1)h}, the digraph G is called a consecutive digraph. In this paper we study the hamiltonicity of endo-Cayley digraphs by using three approaches based on: line digraph, merging cycles and a generalization of the factor group lemma. The results are applied to consecutive digraphs. © 2005 Elsevier B.V. All rights reserved.