Tetravalent normal edge-transitive Cayley graphs on a certain group of order $6n$

Abstract

Let $U_{6n}= \langle a,b|a^{2n}=b^{3}=1,a^{-1}ba=b^{-1}\rangle $ be a groupof order 6n. In this paper tetravalent normal edge-transitive Cayleygraphs on $U_{6n}$ are considered. In this way several nonequivalent normaledge-transitive Cayley graphs on $U_{6n}$ are obtained whose automorphismgroups are given exactly.