A note on commuting graphs for general linear groups

Authors : Maryam NASİRİ, Sayyed Heidar JAFARİ

Pages : 1635-1641

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Publication Date : 2019-12-08

Article Type : Research Paper

Abstract :Let $G$ be a group and $X$ a subset of $G$. Then $\mathcal{C}insert ignore into journalissuearticles values(G, X);$ 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 $\mathcal{C}insert ignore into journalissuearticles values(G, X);$ where $G=GLinsert ignore into journalissuearticles values(n,q);$ and $X$ is the set of transvections.
Keywords : commuting graph, transvections, clique, domination, perfection, planarity