Characterization of \(c\)-circulant digraphs of degree two which are circulant (Q1356734)

A digraph \(G_N(c,\Delta)\) with a positive integer \(N\), a subset \(\Delta\) of \(\mathbb{Z}_N\) and \(0\neq c\in\mathbb{Z}_N\) is called \(c\)-circulant digraph if \(\mathbb{Z}_N\) is the set of vertices and the adjacency rules are given by functions \(x\to cx+a\) with \(a\in\Delta\). The authors give necessary and sufficient conditions for a \(c\)-circular digraph of degree two, \(G_N(c,\{a_1,a_2\})\), to be isomorphic to some circulant digraph \(G_N(1,\{b_1,b_2\})\). Further, they give sufficient conditions for \(G_N(c,\Delta)\) to be a Cayley digraph.