Endo-circulant digraphs: Connectivity and generalized cycles (Q1292822)

Let \(A\) be a finite abelian group and \(\Delta\subset A\). For any endomorphism \(\phi\) of \(A\), the endo-circulant digraph \(G_A(\phi,\Delta)\) is defined to have vertex set \(A\) and edge set \(\{x\to \phi(x)+ a\mid a\in\Delta\}\). When is an endo-circulant digraph connected? In this paper, a necessary and sufficient conditon is given.