Year 2019, Volume 48 , Issue 6, Pages 1635 - 1641 2019-12-08

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
  • [1] P.J. Cameron and Q. Mary, Automorphisms of graphs, London E14Ns, U.K. Draft, 2001.
  • [2] M. Chudnovsky, N. Robertson, P. Seymour and R. Thomas, The strong perfect graph theorem, Ann. of Math. (2), 164 (1), 51–229, 2006.
  • [3] H. Poliatsek, Irreducible Groups Generated by Transvections over Finite Fields of Characteristic Two, J. Algebra, 39, 328–333, 1976.
  • [4] J.J. Rotman, An Introduction to the Theory of groups, Springer-Verlag Newyork, Inc. 1995.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0001-6254-0860
Author: Maryam NASİRİ
Institution: Shahrood University of Technology
Country: Iran


Orcid: 0000-0002-6745-0087
Author: Sayyed Heidar JAFARİ (Primary Author)
Institution: Shahrood University of Technology
Country: Iran


Dates

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 <https://dergipark.org.tr/en/pub/hujms/issue/50516/656657>
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.