normal edge-transitive and $ frac{1}{2}$-arc-transitive cayley graphs on non-abelian groups of order $2pq$ , $p > q$ are primes

normal edge-transitive and $frac{1}{2}-$arc$-$transitive cayley graphs on non-abelian groups of order $2pq$‎, ‎$p > q$ are odd primes

‎darafsheh and assari in [normal edge-transitive cayley graphs on non-abelian groups of order 4p‎, ‎where $p$ is a prime number‎, ‎sci‎. ‎china math‎., ‎56 (1) (2013) 213-219.] classified the connected normal edge transitive and‎ ‎$frac{1}{2}-$arc-transitive cayley graph of groups of order $4p$‎. ‎in this paper we continue this work by classifying the‎ ‎connected cayley graph of groups of order...

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...

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(jh=h ′j; jz(k)j) = 1 = gcd(jk=k ′j; jz(h)j), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

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