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arXiv · 1304.4839

Non-commuting graphs of nilpotent groups

Alireza Abdollahi·Hamid Shahverdi
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Abstract

Let $G$ be a non-abelian group and $Z(G)$ be the center of $G$. The non-commuting graph $\Gamma_G$ associated to $G$ is the graph whose vertex set is $G\setminus Z(G)$ and two distinct elements $x,y$ are adjacent if and only if $xy\neq yx$. We prove that if $G$ and $H$ are non-abelian nilpotent groups with irregular isomorphic non-commuting graphs, then $|G|=|H|$.

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Alireza Abdollahi, Hamid Shahverdi. 2013-04-17. Non-commuting graphs of nilpotent groups. https://arxiv.org/abs/1304.4839

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