‎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...

darafsheh and assari in [normal edge-transitive cayley graphs onnon-abelian groups of order 4p, where p is a prime number, sci. china math. {bf 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 theconnected cayley graph of groups of order $2pq$, $p > q...

‎Let $X=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n\‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the Hankel matrix of size $2times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_Gsubset K[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaula...

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.

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.

‎let $x=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the hankel matrix of size $2times n$ and let $g$ be a closed graph on the vertex set $[n].$ we study the binomial ideal $i_gsubset k[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $x$ which correspond to the edges of $g.$ we show that...

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...

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...

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.