On the eigenvalues of normal edge-transitive Cayley graphs

Abstract

A graph $Gamma$ is said to be vertex-transitive or edge‎- ‎transitive‎ <br />‎if the automorphism group of $Gamma$ acts transitively on $V(Gamma)$ or $E(Gamma)$‎, ‎respectively‎. <br />‎Let $Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$‎. ‎Then, $Gamma$ is said to be normal edge-transitive‎, <br />‎if $N_{Aut(Gamma)}(G)$ acts transitively on edges‎. <br />‎In this paper‎, ‎the eigenvalues of normal edge-transitive Cayley graphs of the groups $D_{2n}$ and $T_{4n}$ are given‎.