A classification of circulant DCI(CI)-digraphs of 2-power order
Let \(Z_n\) be a cyclic group of order \(n\) with unit 0 and let the Cayley graph \(C(Z_n,S)\) be the circulant digraph of \(Z_n\) with respect to \(S\subseteq Z_n\backslash \{0\}\). \(C(Z_n,S)\) is called a circulant DCI-digraph if, for any circulant digraph \(C(Z_n,T), C(Z_n,S)\cong C(Z_n,T)\) implies that \(S\) and \(T\) are conjugate in \(\Aut(Z_n)\), the automorphism group of \(Z_n\), and \(S\) is called a DCI-graph of \(\mathbb{Z}_n\) in this case. A finite group \(G\) is called a DCI-group if any subset \(S\) of \(G \backslash \{1\}\) is a DCI-subset. Otherwise \(G\) is an NDCI-group. The author gives a classification of circulant DCI-digraphs of 2-power order, or in other words, of DCI-subsets of \(\mathbb{Z}_2\).
scientific article; zbMATH DE number 1915536