Feng, Yan Quan; Wang, Dian Jun; Chen, Jing Lin A family of nonnormal Cayley digraphs. (Chinese. English summary) Zbl 1025.05031 Acta Math. Sin. 46, No. 1, 103-108 (2003). Summary: We call a Cayley digraph \(\Gamma= \text{Cay}(G,S)\) normal for \(G\) if \(G_R\), the right regular representation of \(G\), is a normal subgroup of the full automorphism group \(\operatorname{Aut}(\Gamma)\) of \(\Gamma\). In this paper we determine the normality of Cayley digraphs of valency 2 on non-abelian groups of order \(2p^2\) (\(p\) odd prime). As a result, a family of nonnormal Caylay digraphs is found. MSC: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures Keywords:automorphism group; normality PDFBibTeX XMLCite \textit{Y. Q. Feng} et al., Acta Math. Sin. 46, No. 1, 103--108 (2003; Zbl 1025.05031)