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Double-toroidal and triple-toroidal commuting graph

Year 2024, Volume: 53 Issue: 3, 735 - 747, 27.06.2024
https://doi.org/10.15672/hujms.1052964

Abstract

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

References

  • [1] A. Abdollahi, S. Akbari and H. R. Maimani, Non-commuting graph of a group, J. Algebra 298(2), 468–492, 2006.
  • [2] M. Afkhami, M. Farrokhi, K. Khashyarmanesh, Planar, toroidal and projective commuting and non-commuting graphs, Commun. Algebra 43(7), 2964–2970, 2015.
  • [3] S. Akbari, M. Ghandehari, M. Hadian and A. Mohammadian, On commuting graphs of semisimple rings, Linear Algebra Appl. 390, 345–355, 2004.
  • [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] 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] 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] R. Brauer and K. A. Fowler, On groups of even order, Ann. Math. 62(3), 565–583, 1955.
  • [8] A. K. Das, D. Nongsiang, On the genus of the commuting graphs of finite non-abelian groups, IEJA 19, 91–109, 2016.
  • [9] The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.6.4, 2013. (http://www.gap-system.org/).
  • [10] A. Iranmanesh and A. Jafarzadeh, Characterization of finite groups by their commuting graph, Acta Math. Acad. Paedagog. Nyíregyháziensis 23(1), 7–13, 2007.
  • [11] A. R. Moghaddamfar, W. J. Shi, W. Zhou and A. R. Zokayi, On the noncommuting graph associated with a finite group, Sib. Math. J. 46(2), 325–332, 2005.
  • [12] A. Mohammadian, On commuting graphs of finite matrix rings, Commun. Algebra 38(3), 988–994, 2010.
  • [13] B.H. Neumann, A problem of Paul Erdös on groups, J. Aust. Math. Soc. (Series A) 21(4), 467–472, 1976.
  • [14] D. B. West, Introduction to Graph Theory (Second Edition), PHI Learning Private Limited, New Delhi, 2009.
  • [15] A. T. White, Graphs, Groups and Surfaces, North-Holland Mathematics Studies, 8, American Elsevier Publishing Co., Inc., New York, 1973.
Year 2024, Volume: 53 Issue: 3, 735 - 747, 27.06.2024
https://doi.org/10.15672/hujms.1052964

Abstract

References

  • [1] A. Abdollahi, S. Akbari and H. R. Maimani, Non-commuting graph of a group, J. Algebra 298(2), 468–492, 2006.
  • [2] M. Afkhami, M. Farrokhi, K. Khashyarmanesh, Planar, toroidal and projective commuting and non-commuting graphs, Commun. Algebra 43(7), 2964–2970, 2015.
  • [3] S. Akbari, M. Ghandehari, M. Hadian and A. Mohammadian, On commuting graphs of semisimple rings, Linear Algebra Appl. 390, 345–355, 2004.
  • [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] 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] 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] R. Brauer and K. A. Fowler, On groups of even order, Ann. Math. 62(3), 565–583, 1955.
  • [8] A. K. Das, D. Nongsiang, On the genus of the commuting graphs of finite non-abelian groups, IEJA 19, 91–109, 2016.
  • [9] The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.6.4, 2013. (http://www.gap-system.org/).
  • [10] A. Iranmanesh and A. Jafarzadeh, Characterization of finite groups by their commuting graph, Acta Math. Acad. Paedagog. Nyíregyháziensis 23(1), 7–13, 2007.
  • [11] A. R. Moghaddamfar, W. J. Shi, W. Zhou and A. R. Zokayi, On the noncommuting graph associated with a finite group, Sib. Math. J. 46(2), 325–332, 2005.
  • [12] A. Mohammadian, On commuting graphs of finite matrix rings, Commun. Algebra 38(3), 988–994, 2010.
  • [13] B.H. Neumann, A problem of Paul Erdös on groups, J. Aust. Math. Soc. (Series A) 21(4), 467–472, 1976.
  • [14] D. B. West, Introduction to Graph Theory (Second Edition), PHI Learning Private Limited, New Delhi, 2009.
  • [15] A. T. White, Graphs, Groups and Surfaces, North-Holland Mathematics Studies, 8, American Elsevier Publishing Co., Inc., New York, 1973.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Deiborlang Nongsiang 0000-0002-0213-7671

Early Pub Date January 10, 2024
Publication Date June 27, 2024
Published in Issue Year 2024 Volume: 53 Issue: 3

Cite

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