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Double-toroidal and triple-toroidal commuting graph

Yıl 2024, Cilt: 53 Sayı: 3, 735 - 747, 27.06.2024
https://doi.org/10.15672/hujms.1052964

Öz

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

Kaynakça

  • [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.
Yıl 2024, Cilt: 53 Sayı: 3, 735 - 747, 27.06.2024
https://doi.org/10.15672/hujms.1052964

Öz

Kaynakça

  • [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.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Deiborlang Nongsiang 0000-0002-0213-7671

Erken Görünüm Tarihi 10 Ocak 2024
Yayımlanma Tarihi 27 Haziran 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 53 Sayı: 3

Kaynak Göster

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. Haziran 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, sy. 3 (Haziran 2024): 735-47. https://doi.org/10.15672/hujms.1052964.
EndNote Nongsiang D (01 Haziran 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, c. 53, sy. 3, ss. 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 (Haziran 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, c. 53, sy. 3, 2024, ss. 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.