The Solubility Graph Associated With a Finite Group

Abstract

Let $G$ be a finite group. The solubility graph associated with the finite group $G$, denoted by ${\Gamma }_{\mathcal{S}}(G)$, is a simple graph whose vertices are the non-trivial elements of $G$, and there is an edge between two distinct elements $x$ and $y$ if and only if $⟨x,y⟩$ is a soluble subgroup of $G$. In this paper, we examine some properties of solubility graphs.

References in corpus (1)

• A note on solvable graphs of finite groups