the unitary cayley graph xn has vertex set zn = {0, 1,…, n-1} and vertices u and v areadjacent, if gcd(uv, n) = 1. in [a. ilić, the energy of unitary cayley graphs, linear algebraappl. 431 (2009) 1881–1889], the energy of unitary cayley graphs is computed. in this paperthe wiener and hyperwiener index of xn is computed.

The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.

A graph is called symmetric if its full automorphism group acts transitively on the set of arcs. The Cayley graph $Gamma=Cay(G,S)$ on group $G$ is said to be normal symmetric if $N_A(R(G))=R(G)rtimes Aut(G,S)$ acts transitively on the set of arcs of $Gamma$. In this paper, we classify all connected tetravalent normal symmetric Cayley graphs of order $p^2q$ where $p>q$ are prime numbers.

‎In this paper, first we introduce the end of locally finite graphs as an equivalence class of infinite paths in the graph. Then we mention the ends of finitely generated groups using the Cayley graph. It was proved that the number of ends of groups are not depended on the Cayley graph and that the number of ends in the groups is equal to zero, one, two, or infinity. For ...

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...

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...

Let G(V;E) be a graph. The common neighborhood graph (congraph) of G is a graph with vertex set V , in which two vertices are adjacent if and only if they have a common neighbor in G. In this paper, we obtain characteristics of congraphs under graph operations; Graph :::::union:::::, Graph cartesian product, Graph tensor product, and Graph join, and relations between Cayley graphs and its c...

A graph X is max-λ if λ(X) = δ(X). A graph X is super-λ if X is max-λ and every minimum edge-cut set of X isolates one vertex. In this paper, we proved that for all but a few exceptions, the mixed Cayley graph which is defined as a new kind of semi-regular graph is max-λ and super-λ. c © 2008 Elsevier B.V. All rights reserved.

Abstract : We call a Cayley graph Γ = Cay (G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aut(Γ). In this paper, a classification of all non-normal Cayley graphs of finite abelian group with valency 6 was presented.  

‎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...