Automorphism Groups of Tetravalent Cayley Graphs on Regular \(5\)-Groups

Abstract

In [2] it is proved that if \(X = Cay(G, S)\) is a connected tetravalent Cayley graph on a regular \(p\)-group \(G\) (for \(p \neq 2, 5\)), then the right regular representation of \(G\) is normal in the automorphism group of \(X\). In this paper, we prove that a similar result holds, for \(p = 5\), under a slightly stronger hypothesis. Some remarkable examples are presented.