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

Azad, Azizollah; Elahinezhad, Nafiseh

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

Authors

Arak University

Abstract

Let

G

be a non-abelian group and let

Z (G)

be the center of

G

. Associate with

G

there is a
graph

Γ_{G}

as follows: Take

G ∖ Z (G)

as vertices of

Γ_{G}

and joint two distinct vertices

x

and

y

whenever

y x \neq y x

Γ_{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

Γ_{P S L (2, q)}

, where

q \equiv 0 (m o d 4)

. In this paper we will compute the Szeged index for

Γ_{P S L (2, q)}

, where

q ≢ 0 (m o d 4)

Keywords

References

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