Order divisor graphs of finite groups

TL;DR

This paper introduces order divisor graphs for finite groups, where vertices are group elements and edges connect elements with divisible orders, exploring their properties and structure within algebraic graph theory.

Contribution

It defines and studies a new class of graphs based on divisibility of element orders in finite groups, expanding the interplay between group theory and graph theory.

Findings

Characterization of order divisor graphs

Connections to existing graph classes

Potential applications in group theory analysis

Abstract

The interplay between groups and graphs have been the most famous and productive area of algebraic graph theory. In this paper, we introduce and study the graphs whose vertex set is group G such that two distinct vertices a and b having different orders are adjacent provided that o(a) divides o(b) or o(b) divides o(a).