Commutativity pattern of finite non-abelian $p$-groups determine their orders

A. Abdollahi, S. Akbari, H. Dorbidi +1

Let $G$ be a non-abelian group and $Z(G)$ be the center of $G$. Associate a graph ${\Gamma }_G$ (called non-commuting graph of $G$) with $G$ as follows: take $G\setminus Z(G)$ as the verti…