On the normality of Cayley digraphs of valency 2 on non-abelian group of odd order
A Cayley digraph \(\Gamma= \text{Cay}(G, S)\) is called normal if the right regular representation \(G_R\) of \(G\) is a normal subgroup of \(\Aut\Gamma\). In this paper, Cayley digraphs of valency 2 on non-abelian groups of odd order are considered. The authors prove that such a graph \(\text{Cay}(G, S)\) is normal if the automorphism group of a graph \(A(\Gamma)\), constructed in this paper, is primitive on its vertex set. Moreover, the authors obtain the result that Cayley digraphs of valency 2 on non-abelian groups of order \(pq^2\) are normal if \(p\), \(q\) are distinct odd prime numbers.
scientific article; zbMATH DE number 1507470