چکیده انگلیسی:
Let $G$ be a non-abelian group and let $Z(G)$ be the center of $G$. Associate with $G$ there is a graph $Gamma_G$ as follows: Take $Gsetminus Z(G)$ as vertices of $Gamma_G$ and joint two distinct vertices $x$ and $y$ whenever $yxneq yx$. $Gamma_G$ is called the non-commuting graph of $G$. In recent years many interesting works have been done in non-commutative graph of groups. Computing the clique number, chromatic number, Szeged index and Wiener index play important role in graph theory. In particular, the clique number of non-commuting graph of some the general linear groups has been determined.
nt Recently, Wiener and Szeged indices have been computed for $Gamma_{PSL(2,q)}$, where $qequiv 0 (mod ~~4)$. In this paper we will compute the Szeged index for $Gamma_{PSL(2,q)}$, where $qnotequiv 0 (mod ~~ 4)$.
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