On endo-Cayley digraphs: The hamiltonian property

Given a finite abelian group A, a subset Δ⊆A and an endomorphism φ of A, the endo-Cayley digraph GA(φ,Δ) is defined by taking A as the vertex set and making every vertex x adjacent to the vertices φ(x)+a with a∈Δ. When A is cyclic and the set Δ is of the form Δ={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.