Some characterizatsion of coprime graph of dihedral group D 2n

Abstract

The Coprime graph of group G denoted Γ G is a graph with vertices is an element of G, and two distinct vertices are adjacent when its order relative prime. In 2020, Gazir et al. give some characterizations of Γ D 2n for n a prime power. The method that uses in this paper is deductive proof by taking some example of a coprime graph of D 2n , then generalized the characterization of example. This paper gives some characteristics of the coprime graph of a dihedral group for more general cases. One of the result, Γ D 2n is a multipartite graph with girth 3, radius 1, and diameter 2.