Endo-circulant digraphs: connectivity and generalized cycles Original Research Article

Given a finite abelian group A, a subset δ ⊂ A and an endomorphism φ of A, the endo-circulant digraph GA(φ, δ) is defined by taking A as vertex set and every vertex x adjacent to the vertices of the form φ(x) + a with a ∈ δ. In this paper, the endo-circulant digraphs which are strongly connected are characterized and so are those that are generalized cycles. Moreover, a sufficient condition is obtained for an endo-circulant digraph to be a Cayley digraph.