- Hacettepe Journal of Mathematics and Statistics
- Vol: 48 Issue: 6
- A note on commuting graphs for general linear groups
A note on commuting graphs for general linear groups
Authors : Maryam Nasiri, Sayyed Heidar Jafari
Pages : 1635-1641
View : 12 | Download : 5
Publication Date : 2019-12-08
Article Type : Research
Abstract :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.Keywords : commuting graph, transvections, clique, domination, perfection, planarity