Some Properties of Coprime Graph of Dihedral Group D_2n When n is a Prime Power
Abdul Gazir Syarifudin, I Gede Adhitya Wisnu Wardhana, Ni Wayan Switrayni, Qurratul Aini · Journal of Fundamental Mathematics and Applications (JFMA) · 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 \Gamma_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 \Gamma_D_2n is a complete bipartite graph. Moreover, if n is the power of prime then \Gamma_D_2n is a multipartite graph.