On the isomorphisms and automorphism groups of circulants (Q1915144)

Let \(M\) be a minimal generating set of the cyclic group \(Z_n\) and let \(\widetilde M = \{m, - m \mid m \in M\}\). Let \(M \subseteq S \subseteq \widetilde M\). The authors prove that if a circulant digraph of order \(n\) with symbol \(T\) is isomorphic to the circulant digraph of order \(n\) with symbol \(S\), then there exists an \(a \in Z^*_n\) such that \(T = aS\). They also determine the automorphism group of the circulant digraph with symbol \(S\).