Abstract
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.
Highlights
Study of algebraic structures represented in a graphs raises many recent and in interesting results
We will study some properties of coprime graph of a dihedral group
For any u ∈ Vi dan v ∈ Vj where i = j we have (|u|, |v|) = 1, u and v are adjacent so the coprime graph of the dihedral group is complete tripartite graph
Summary
Study of algebraic structures represented in a graphs raises many recent and in interesting results. This area is relatively new, and over the years different types of graphs of a group were defined. In 2014, Ma et al define a coprime graph of a group [1]. The coprime graph of a group G, denoted by ΓG is a graph whose vertices are elements of G and two distinct vertices a and b are adjacent if only if (|a|, |b|) = 1 [2]. We will study some properties of coprime graph of a dihedral group
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
