On the Szeged and Eccentric connectivity indices of non-commutative graph of finite groups

Document Type : Research Articles

Authors

Arak University

Abstract

Let

G

be a non-abelian group.
The non-commuting graph

G a m m a_{G}

G

is defined as the graph whose vertex set is the non-central elements of

G

and two vertices are joined if and only if they do not commute.

In this paper we study some properties of

G a m m a_{G}

and introduce

n

-regular

A C

-groups. Also we then obtain a formula for Szeged index of

G a m m a_{G}

in terms of

n

| Z (G) |

and

| G |

.
Moreover, we determine eccentric connectivity index of

G a m m a_{G}

for every non-abelian finite group

G

in terms of the number of conjugacy classes

k (G)

and the size of the group

G

Keywords