Azad, A., Elahinezhad, N. (2014). ON THE SZEGED INDEX OF NON-COMMUTATIVE GRAPH OF GENERAL LINEAR GROUP. Algebraic Structures and Their Applications, 1(2), 105-115.

Azizollah Azad; Nafiseh Elahinezhad. "ON THE SZEGED INDEX OF NON-COMMUTATIVE GRAPH OF GENERAL LINEAR GROUP". Algebraic Structures and Their Applications, 1, 2, 2014, 105-115.

Azad, A., Elahinezhad, N. (2014). 'ON THE SZEGED INDEX OF NON-COMMUTATIVE GRAPH OF GENERAL LINEAR GROUP', Algebraic Structures and Their Applications, 1(2), pp. 105-115.

Azad, A., Elahinezhad, N. ON THE SZEGED INDEX OF NON-COMMUTATIVE GRAPH OF GENERAL LINEAR GROUP. Algebraic Structures and Their Applications, 2014; 1(2): 105-115.

ON THE SZEGED INDEX OF NON-COMMUTATIVE GRAPH OF GENERAL LINEAR GROUP

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 $G\setminus Z(G)$ as vertices of $\Gamma_G$ and joint two distinct vertices $x$ and $y$ whenever $yx\neq yx$. $\Gamma_G$ 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 $q\equiv 0 (mod ~~4)$. In this paper we will compute the Szeged index for $\Gamma_{PSL(2,q)}$, where $q\not\equiv 0 (mod ~~ 4)$.

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