Tetravalent Non-Normal Cayley Graphs of Order $4p$

Tetravalent Non-Normal Cayley Graphs of Order 4p

A Cayley graph Cay(G,S) on a group G is said to be normal if the right regular representation R(G) of G is normal in the full automorphism group of Cay(G,S). In this paper, all connected tetravalent non-normal Cayley graphs of order 4p are constructed explicitly for each prime p. As a result, there are fifteen sporadic and eleven infinite families of tetravalent non-normal Cayley graphs of orde...

Tetravalent half-edge-transitive graphs and non-normal Cayley graphs

Normal edge-transitive Cayley graphs on the non-abelian groups of order $4p^2$, where $p$ is a prime number

In this paper, we determine all of connected normal edge-transitive Cayley graphs on non-abelian groups with order $4p^2$, where $p$ is a prime number.

Product of normal edge-transitive Cayley graphs

For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

On the eigenvalues of normal edge-transitive Cayley graphs

A graph $Gamma$ is said to be vertex-transitive or edge‎- ‎transitive‎ ‎if the automorphism group of $Gamma$ acts transitively on $V(Gamma)$ or $E(Gamma)$‎, ‎respectively‎. ‎Let $Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$‎. ‎Then, $Gamma$ is said to be normal edge-transitive‎, ‎if $N_{Aut(Gamma)}(G)$ acts transitively on edges‎. ‎In this paper‎, ‎the eigenvalues of normal edge-tra...