SOME PROPERTIES OF COPRIME GRAPH OF DIHEDRAL GROUP D_2n WHEN n IS A PRIME POWER - Abdul Gazir S; I Gede Adhitya Wisnu Wardhana; Ni Wayan Switrayni; Qurratul Aini (Diponegoro University, 2020)
The Study of algebraic structures, especially on graphs theory, leads to anew topics of research in recent years. In this paper, the algebraic structures that will be represented by a coprime graph are the dihedral group and its subgroups. The coprime graph of a group G, denoted by Γ_D_2n is a graph whose vertices are elements of G and two distinct vertices a and b are adjacent if only if (|a,|b|)=1. Some properties of the coprime graph of a dihedral group D_2n are obtained. One of the results is if n is prime then Γ_D_2n is a complete bipartite graph. Moreover, if n is the power of prime then Γ_D_2n is a multipartite graph.