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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
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.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $G$ be a group and $X$ a subset of $G$.
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Key Findings & Data: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 $xy=yx$.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:commuting graph · transvections · clique
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.
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Cite This Article
Nasiri, M., Jafari, S. H. (2022). A note on commuting graphs for general linear groups. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 6, 1635–1640. https://ajindex.com/articles/529755