Two mathematical fields that concentrate on creating and analyzing structures are algebra
and graph theory. There are numerous studies linking algebraic structures like groups, rings …

Given a finite group G, the co-prime order graph of G is the simple undirected graph whose
vertex set is G, and two distinct vertices x; y are adjacent if gcd (o (x); o (y))= 1 or p, where p …

For a finite group $ G $ the co-prime graph $\Gamma (G) $ is defined as a graph with vertex
set $ G $ in which two distinct vertices $ x $ and $ y $ are adjacent if and only if $ gcd (o (x) …

Objective: To explore the algebraic structures inherent in groups and their relationship to
graph theory, particularly focusing on the process of converting a group into a graph …

The co-prime order graph of a finite group G is an undirected graph whose vertex set is G
and two distinct vertices u, v∈ G are adjacent if gcd (o (u), o (v))= 1 or a prime number …