Some results in a new power graphs in finite groups

TL;DR

This paper introduces a new type of power graph for finite groups and investigates its connectivity, diameter, and clique number to understand its structural properties.

Contribution

It defines a novel power graph for finite groups and analyzes key graph-theoretic properties, expanding understanding of group structures through graph theory.

Findings

Analysis of connectivity properties

Determination of diameter bounds

Evaluation of clique numbers

Abstract

The power graph of a group is the graph whose vertex set is the set of non-trivial elements of group, two elements being adjacent if one is a power of the other. We define a new power graph and study on connectivity, diameter and clique number of this graphs.