Investigation of Certain Topological Indices in Non-commuting Graph

Jahandideh Khangheshlaghi, Marya,m; Shokrollahi Yancheshmeh, Sara

doi:10.22055/jamm.2026.50736.2419

Investigation of Certain Topological Indices in Non-commuting Graph

Document Type : Original Paper

Authors

Marya,m Jahandideh Khangheshlaghi ¹

Sara shokrollahi Yancheshmeh ²

¹ Department of Mathematics, Mahs.C., Islamic Azad University, Mahshahr, Iran

² Department of Mathematics, Ahv.C., Islamic Azad University, Ahwaz, Iran

10.22055/jamm.2026.50736.2419

Abstract

Abstract
Let G be a finite non-abelian group. The non-commuting graph of G , denoted by Γ(G) , is defined as the graph whose vertex set is G-Z(G), where two distinct vertices x,yϵV(Γ(G)) are adjacent whenever xy≠yx . In this paper, several topological indices of Γ(G) are investigated, including F-Leap, F_1-Leap and the first and second generalized Zagreb. These indices are analyzed and calculated based on criteria such as distance between vertices, connectivity number, degree of vertices, and eccentricity number. The results of this research can play an effective role in better understanding the structural characteristics of groups and their relationship with topological indices.

Keywords

Non – commuting graph

F- Leap index

F_1 – Leap index

The Zagreb indices

The generalized Zagreb indices

Subjects