@article {
author = {Ahanjideh, Neda and Iranmanesh, A.},
title = {On the relation between the non-commuting graph and the prime graph},
journal = {International Journal of Group Theory},
volume = {1},
number = {1},
pages = {25-28},
year = {2012},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2012.469},
abstract = {$\pi(G)$ denote the set of prime divisors of the order of $G$ and denote by $Z(G)$ the center of $G$. The\textit{ prime graph} of $G$ is the graph with vertex set $\pi(G)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $G$ contains an element of order $pq$ and the \textit{non-commuting graph} of $G$ is the graph with the vertex set $G-Z(G)$ where two non-central elements $x$ and $y$ are joined by an edge if and only if $xy \neq yx$. Let $ G $ and $ H $ be non-abelian finite groups with isomorphic non-commuting graphs. In this article, we show that if $ | Z ( G ) | = | Z ( H ) | $, then $ G $ and $ H $ have the same prime graphs and also, the set of orders of the maximal abelian subgroups of $ G $ and $ H $ are the same.},
keywords = {Non-commuting graph,Prime graph, Maximal abelian subgroups, Maximal independent
set of the graph},
url = {https://ijgt.ui.ac.ir/article_469.html},
eprint = {https://ijgt.ui.ac.ir/article_469_92246b683ed4fb19f106761cb0e6d800.pdf}
}