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## A note on commuting graphs for general linear groups

#### Maryam NASİRİ [1] , Sayyed Heidar JAFARİ [2]

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.
commuting graph, transvections, clique, domination, perfection, planarity
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• [3] H. Poliatsek, Irreducible Groups Generated by Transvections over Finite Fields of Characteristic Two, J. Algebra, 39, 328–333, 1976.
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Primary Language en Mathematics Mathematics Orcid: 0000-0001-6254-0860Author: Maryam NASİRİ Institution: Shahrood University of TechnologyCountry: Iran Orcid: 0000-0002-6745-0087Author: Sayyed Heidar JAFARİ (Primary Author)Institution: Shahrood University of TechnologyCountry: Iran Publication Date : December 8, 2019
 Bibtex @research article { hujms656657, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1635 - 1641}, doi = {}, title = {A note on commuting graphs for general linear groups}, key = {cite}, author = {NASİRİ, Maryam and JAFARİ, Sayyed Heidar} } APA NASİRİ, M , JAFARİ, S . (2019). A note on commuting graphs for general linear groups. Hacettepe Journal of Mathematics and Statistics , 48 (6) , 1635-1641 . Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/50516/656657 MLA NASİRİ, M , JAFARİ, S . "A note on commuting graphs for general linear groups". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1635-1641 Chicago NASİRİ, M , JAFARİ, S . "A note on commuting graphs for general linear groups". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1635-1641 RIS TY - JOUR T1 - A note on commuting graphs for general linear groups AU - Maryam NASİRİ , Sayyed Heidar JAFARİ Y1 - 2019 PY - 2019 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1635 EP - 1641 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics A note on commuting graphs for general linear groups %A Maryam NASİRİ , Sayyed Heidar JAFARİ %T A note on commuting graphs for general linear groups %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R %U ISNAD NASİRİ, Maryam , JAFARİ, Sayyed Heidar . "A note on commuting graphs for general linear groups". Hacettepe Journal of Mathematics and Statistics 48 / 6 (December 2019): 1635-1641 . AMA NASİRİ M , JAFARİ S . A note on commuting graphs for general linear groups. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1635-1641. Vancouver NASİRİ M , JAFARİ S . A note on commuting graphs for general linear groups. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1641-1635.