Proof of a conjecture of Abdollahi-Akbari-Maimani concerning the non-commutative graph of finite groups

Luis A. Dupont, Daniel G. Mendoza, Armando Sánchez-Nungaray

The non--commuting graph $\Gamma (G)$ of a non--abelian group $G$ is defined as follows. The vertex set $V(\Gamma (G))$ of $\Gamma (G)$ is $G\setminus Z(G)$ where $Z(G)$ denotes the center of $G$ an…