product of normal edge-transitive cayley graphs

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.

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 ′|, |Z(K)|) = 1 = gcd(|K/K′|, |Z(H)|), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive. c ⃝ 2014 IAUCTB. All rights reserved.

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...

Quotients of Normal Edge-Transitive Cayley Graphs

The symmetry properties of mathematical structures are often important for understanding these structures. Graphs sometimes have a large group of symmetries, especially when they have an algebraic construction such as the Cayley graphs. These graphs are constructed from abstract groups and are vertex-transitive and this is the reason for their symmetric appearance. Some Cayley graphs have even ...

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...

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