Normal Cayley graphs of finite groups
Let \(G\) be a finite group, \(S\) a non-empty subset of \(G\) not containing the identity and \(X= \text{Cay}(G,S)\), the Cayley digraph of \(G\) with respect to \(S\). A Cayley digraph \(X= \text{Cay}(G,S)\) is said to be normal if \(R(G)\triangleleft A= \Aut(X)\), where \(R(G)\) is the right regular representation of \(G\). A group is said to have a normal Cayley digraph if \(G\) has a subset \(S\) such that the Cayley digraph \(\text{Cay}(G,S)\) is normal. The main result of this paper is that every finite group has a normal Cayley digraph.
scientific article; zbMATH DE number 1187424