Endo-circulant digraphs of degree two and Cayley digraphs on finite abelian groups

We extend the characterization of the c-circulant digraphs of degree two which are circulant to the endo-circulant digraphs. As a consequence, an arithmetic characterization of the endo-circulant digraphs which are circulant is obtained. Moreover, a theorem by Delorme et al. describing the Ádám isomorphisms for Cayley digraphs on finite abelian groups is seen from the point of view of isomorphic endo-circulant digraphs.