On the connectivity of enhanced power graph of finite group

TL;DR

This paper investigates the vertex connectivity of enhanced power graphs of finite groups, providing classifications, bounds, and characterizations for both abelian and certain non-abelian groups.

Contribution

It offers a comprehensive classification and bounds for the vertex connectivity of enhanced power graphs of finite groups, including abelian and specific non-abelian cases.

Findings

Classified abelian groups with vertex connectivity 1

Derived upper bounds for vertex connectivity in abelian groups

Characterized when the proper enhanced power graph is connected

Abstract

This paper deals with the vertex connectivity of enhanced power graph of finite group. We classify all abelian groups G such that vertex connectivity of enhanced power graph of G is 1. We derive an upper bound of vertex connectivity for the enhanced power graph of any general abelian group G. Also we completely characterize all abelian group G, such that the proper enhanced power graph is connected. Moreover, we study some special class of non-abelian group G such that the proper enhanced power graph is connected and we find their vertex connectivity.