Hacettepe Journal of Mathematics and Statistics 2651-477X 2651-477X Hacettepe University Mathematical Sciences Matematik A note on commuting graphs for general linear groups https://orcid.org/0000-0001-6254-0860 Nasiri Maryam Shahrood University of Technology https://orcid.org/0000-0002-6745-0087 Jafari Sayyed Heidar Shahrood University of Technology 12 08 2019 48 6 1635 1641 09 18 2017 05 23 2018 Copyright © 2002, Hacettepe Journal of Mathematics and Statistics 2002 Hacettepe Journal of Mathematics and Statistics

Let $G$ be a group and $X$ a subset of $G$. Then $\mathcal{C}(G, X)$ is a graph with vertex set $X$ in which two distinct elements $x$, $y\in X$ are joined by an edge if $xy=yx$. In this paper, we study the clique number, the domination number, the diameter, the planarity, the perfection and regularity of $\mathcal{C}(G, X)$ where $G=GL(n,q)$ and $X$ is the set of transvections.

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