A note on the coprime graph of a group

Abstract

In this paper we study the coprime graph of a group $G$. The coprime graph of a group $G$, is a graph whose vertices are elements of $G$ and two distinct vertices $x$ and $y$ are adjacent iff $(|x|,|y|)=1$. In this paper we classify all the groups which the coprime graph is a complete r-partite graph or a planar graph. Also we study the automorphism group of the coprime graph.

Keywords

• coprime graph
• Planner graph
• Automorphism group