Some results of the non-coprime graph of a generalized quaternion group for some n

Abstract

In recent years, the graph used as a representation of a finite group. One kind of graph that represents a finite group is the non-coprime graph. The non-coprime graph of a finite group is simple graph where vertices are all elements of that group without identity element and two distinct vertices are adjacent if and only if its order is not coprime. In this research, we will discuss the non-coprime graph of a generalized quaternion group and its properties. The method that is used is to study literature and analyze it by finding patterns in various examples. The results of this research are the form of the graph, degree of each vertex, radius, diameter, girth, and total of cycles contained in the graph when n = 2k and n an odd prime number.