Automorphism groups and isomorphisms of Cayley digraphs
Let \(G\) be a finite group and \(S\) a subset of \(G\), not containing the identity element 1. The Cayley digraph \(X=\text{Cay} (G,S)\) is defined by \(V(X)=G\) and \(E(X)=\{(g,sg)\;|\;g\in G,\;s\in S\}\). A subset \(S\) of \(G\) is called a CI-subset of \(G\), if for any subset \(T\) of \(G\) with \(\text{Cay} (G,S)\) isomorphic to \(\text{Cay} (G,T)\), there exists \(\alpha \in\Aut(G)\) such that \(S^\alpha=T\). A number of results on Cayley digraphs is obtained, for example, Proposition 3.5: Let \(G\) be a finite group and \(p\) the least divisor of \(|G|\). Let \(S\) be a generating set of \(G\) with \(|S|<p\). Then \(S\) is a CI-subset.
scientific article; zbMATH DE number 1121505
scientific article