Research Article

Double-toroidal and triple-toroidal commuting graph

Volume: 53 Number: 3 June 27, 2024
EN

Double-toroidal and triple-toroidal commuting graph

Abstract

In this paper, all finite non-abelian groups whose commuting graphs can be embed on the double-torus or triple-torus are classified.

Keywords

References

  1. [1] A. Abdollahi, S. Akbari and H. R. Maimani, Non-commuting graph of a group, J. Algebra 298(2), 468–492, 2006.
  2. [2] M. Afkhami, M. Farrokhi, K. Khashyarmanesh, Planar, toroidal and projective commuting and non-commuting graphs, Commun. Algebra 43(7), 2964–2970, 2015.
  3. [3] S. Akbari, M. Ghandehari, M. Hadian and A. Mohammadian, On commuting graphs of semisimple rings, Linear Algebra Appl. 390, 345–355, 2004.
  4. [4] S. Akbari, A. Mohammadian, H. Radjavi and P. Raja, On the diameters of commuting graphs, Linear Algebra Appl. 418(1), 161–176, 2006.
  5. [5] C. Bates, D. Bundy, S. Hart and P. Rowley, A Note on Commuting Graphs for Symmetric Groups, Electron. J. Comb. 16(1), 1–13, 2009.
  6. [6] J. Battle, F. Harary, Y. Kodama and J. W. T. Youngs, Additivity of the genus of a graph, Bull. Amer. Math. Soc. 68, 565–568, 1962.
  7. [7] R. Brauer and K. A. Fowler, On groups of even order, Ann. Math. 62(3), 565–583, 1955.
  8. [8] A. K. Das, D. Nongsiang, On the genus of the commuting graphs of finite non-abelian groups, IEJA 19, 91–109, 2016.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Early Pub Date

January 10, 2024

Publication Date

June 27, 2024

Submission Date

January 3, 2022

Acceptance Date

July 31, 2023

Published in Issue

Year 2024 Volume: 53 Number: 3

APA
Nongsiang, D. (2024). Double-toroidal and triple-toroidal commuting graph. Hacettepe Journal of Mathematics and Statistics, 53(3), 735-747. https://doi.org/10.15672/hujms.1052964
AMA
1.Nongsiang D. Double-toroidal and triple-toroidal commuting graph. Hacettepe Journal of Mathematics and Statistics. 2024;53(3):735-747. doi:10.15672/hujms.1052964
Chicago
Nongsiang, Deiborlang. 2024. “Double-Toroidal and Triple-Toroidal Commuting Graph”. Hacettepe Journal of Mathematics and Statistics 53 (3): 735-47. https://doi.org/10.15672/hujms.1052964.
EndNote
Nongsiang D (June 1, 2024) Double-toroidal and triple-toroidal commuting graph. Hacettepe Journal of Mathematics and Statistics 53 3 735–747.
IEEE
[1]D. Nongsiang, “Double-toroidal and triple-toroidal commuting graph”, Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 3, pp. 735–747, June 2024, doi: 10.15672/hujms.1052964.
ISNAD
Nongsiang, Deiborlang. “Double-Toroidal and Triple-Toroidal Commuting Graph”. Hacettepe Journal of Mathematics and Statistics 53/3 (June 1, 2024): 735-747. https://doi.org/10.15672/hujms.1052964.
JAMA
1.Nongsiang D. Double-toroidal and triple-toroidal commuting graph. Hacettepe Journal of Mathematics and Statistics. 2024;53:735–747.
MLA
Nongsiang, Deiborlang. “Double-Toroidal and Triple-Toroidal Commuting Graph”. Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 3, June 2024, pp. 735-47, doi:10.15672/hujms.1052964.
Vancouver
1.Deiborlang Nongsiang. Double-toroidal and triple-toroidal commuting graph. Hacettepe Journal of Mathematics and Statistics. 2024 Jun. 1;53(3):735-47. doi:10.15672/hujms.1052964

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