Research Article
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Year 2020, Volume: 49 Issue: 6, 1915 - 1925, 08.12.2020
https://doi.org/10.15672/hujms.540309

Abstract

References

  • [1] A. Abdollahi, Commuting graphs of full matrix rings over finite fields, Linear Algebra Appl. 428, 2947–2954, 2008.
  • [2] M. Afkhami, Z. Barati, N. Hoseini and K. Khashyarmanesh, A generalization of commuting graphs, Discrete Math. Algorithm. Appl. 7 (1), 1450068 (11 pages), 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.M. Buckley, D. Machale, and A.N. Sh´e, Finite rings with many commuting pairs of elements, available at http://archive.maths.nuim.ie/staff/sbuckley/Papers/ bms.pdf.
  • [5] J. Dutta and R.K. Nath, Rings having four distinct centralizers, Matrix, M. R. Publications, Assam, 2017, pp. 12–18, Ed. P. Begum.
  • [6] P. Dutta and R.K. Nath, A generalization of commuting probability of finite rings, Asian-European J. Math. 11 (2), 1850023 (15 pages), 2018.
  • [7] P. Dutta and R.K. Nath, On relative commuting probability of finite rings, Miskolc Math. Notes 20 (1), 225–232, 2019.
  • [8] J. Dutta, D.K. Basnet and R.K. Nath, On commuting probability of finite rings, Indag. Math. 28 (2), 272–282, 2017.
  • [9] J. Dutta, D.K. Basnet and R.K. Nath, On generalized non-commuting graph of a finite ring, Algebra Colloq. 25 (1), 149–160, 2018.
  • [10] J. Dutta, D.K. Basnet and R.K. Nath, A note on n-centralizer finite rings, An. Stiint. Univ. Al. I. Cuza Iasi Math. LXIV (f.1), 161–171, 2018.
  • [11] J. Dutta, D.K. Basnet and R.K. Nath, Characterizing some rings of finite order, submitted for publication, available at https://arxiv.org/pdf/1510.08207.pdf.
  • [12] J. Dutta, W.N.T. Fasfous and R.K. Nath, Spectrum and genus of commuting graphs of some classes of finite rings, Acta Comment. Univ. Tartu. Math. 23 (1), 5–12, 2019.
  • [13] A. Erfanian, K. Khashyarmanesh and Kh. Nafar, Non-commuting graphs of rings, Discrete Math. Algorithm. Appl. 7 (3), 1550027 (7 pages), 2015.
  • [14] S.C. Gong, X. Li, G.H. Xu, I. Gutman and B. Furtula, Borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 74, 321–332, 2015.
  • [15] I. Gutman, Hyperenergetic molecular graphs, J. Serb. Chem. Soc. 64, 199–205, 1999.
  • [16] D. MacHale, Commutativity in finite rings, Amer. Math. Monthly, 83, 30–32, 1976.
  • [17] A. Mohammadian, On commuting graphs of finite matrix rings, Comm. Algebra 38, 988–994, 2010.
  • [18] R.K. Nath, Various spectra of commuting graphs of n-centralizer finite groups, J. Eng. Science and Tech. 10 (2S), 170–172, 2018.
  • [19] R.K. Nath, A note on super integral rings, Bol. Soc. Paran. Mat. 38 (4), 213–218, 2020.
  • [20] G.R. Omidi and E. Vatandoost, On the commuting graph of rings, J. Algebra Appl. 10 (3), 521–527, 2011.
  • [21] F. Tura, L-borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 77, 37–44, 2017.
  • [22] E. Vatandoost and F. Ramezani, On the commuting graph of some non-commutative rings with unity, J. Linear Topological Algebra, 5 (4), 289–294, 2016.
  • [23] E. Vatandoost, F. Ramezani and A. Bahraini, On the commuting graph of noncommutative rings of order $p^n q$, J. Linear Topological Algebra, 3 (1), 1–6, 2014.
  • [24] H.B. Walikar, H.S. Ramane and P.R. Hampiholi, On the energy of a graph, Graph Connections, Eds. R. Balakrishnan, H.M. Mulder, A. Vijayakumar., pp. 120–123, Allied Publishers, New Delhi, 1999.

Various spectra and energies of commuting graphs of finite rings

Year 2020, Volume: 49 Issue: 6, 1915 - 1925, 08.12.2020
https://doi.org/10.15672/hujms.540309

Abstract

The commuting graph of a non-commutative ring $R$ with center $Z(R)$ is a simple undirected graph whose vertex set is $R\setminus Z(R)$ and two vertices $x, y$ are adjacent if and only if $xy = yx$. In this paper, we compute various spectra and energies of commuting graphs of some classes of finite rings and study their consequences.

References

  • [1] A. Abdollahi, Commuting graphs of full matrix rings over finite fields, Linear Algebra Appl. 428, 2947–2954, 2008.
  • [2] M. Afkhami, Z. Barati, N. Hoseini and K. Khashyarmanesh, A generalization of commuting graphs, Discrete Math. Algorithm. Appl. 7 (1), 1450068 (11 pages), 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.M. Buckley, D. Machale, and A.N. Sh´e, Finite rings with many commuting pairs of elements, available at http://archive.maths.nuim.ie/staff/sbuckley/Papers/ bms.pdf.
  • [5] J. Dutta and R.K. Nath, Rings having four distinct centralizers, Matrix, M. R. Publications, Assam, 2017, pp. 12–18, Ed. P. Begum.
  • [6] P. Dutta and R.K. Nath, A generalization of commuting probability of finite rings, Asian-European J. Math. 11 (2), 1850023 (15 pages), 2018.
  • [7] P. Dutta and R.K. Nath, On relative commuting probability of finite rings, Miskolc Math. Notes 20 (1), 225–232, 2019.
  • [8] J. Dutta, D.K. Basnet and R.K. Nath, On commuting probability of finite rings, Indag. Math. 28 (2), 272–282, 2017.
  • [9] J. Dutta, D.K. Basnet and R.K. Nath, On generalized non-commuting graph of a finite ring, Algebra Colloq. 25 (1), 149–160, 2018.
  • [10] J. Dutta, D.K. Basnet and R.K. Nath, A note on n-centralizer finite rings, An. Stiint. Univ. Al. I. Cuza Iasi Math. LXIV (f.1), 161–171, 2018.
  • [11] J. Dutta, D.K. Basnet and R.K. Nath, Characterizing some rings of finite order, submitted for publication, available at https://arxiv.org/pdf/1510.08207.pdf.
  • [12] J. Dutta, W.N.T. Fasfous and R.K. Nath, Spectrum and genus of commuting graphs of some classes of finite rings, Acta Comment. Univ. Tartu. Math. 23 (1), 5–12, 2019.
  • [13] A. Erfanian, K. Khashyarmanesh and Kh. Nafar, Non-commuting graphs of rings, Discrete Math. Algorithm. Appl. 7 (3), 1550027 (7 pages), 2015.
  • [14] S.C. Gong, X. Li, G.H. Xu, I. Gutman and B. Furtula, Borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 74, 321–332, 2015.
  • [15] I. Gutman, Hyperenergetic molecular graphs, J. Serb. Chem. Soc. 64, 199–205, 1999.
  • [16] D. MacHale, Commutativity in finite rings, Amer. Math. Monthly, 83, 30–32, 1976.
  • [17] A. Mohammadian, On commuting graphs of finite matrix rings, Comm. Algebra 38, 988–994, 2010.
  • [18] R.K. Nath, Various spectra of commuting graphs of n-centralizer finite groups, J. Eng. Science and Tech. 10 (2S), 170–172, 2018.
  • [19] R.K. Nath, A note on super integral rings, Bol. Soc. Paran. Mat. 38 (4), 213–218, 2020.
  • [20] G.R. Omidi and E. Vatandoost, On the commuting graph of rings, J. Algebra Appl. 10 (3), 521–527, 2011.
  • [21] F. Tura, L-borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 77, 37–44, 2017.
  • [22] E. Vatandoost and F. Ramezani, On the commuting graph of some non-commutative rings with unity, J. Linear Topological Algebra, 5 (4), 289–294, 2016.
  • [23] E. Vatandoost, F. Ramezani and A. Bahraini, On the commuting graph of noncommutative rings of order $p^n q$, J. Linear Topological Algebra, 3 (1), 1–6, 2014.
  • [24] H.B. Walikar, H.S. Ramane and P.R. Hampiholi, On the energy of a graph, Graph Connections, Eds. R. Balakrishnan, H.M. Mulder, A. Vijayakumar., pp. 120–123, Allied Publishers, New Delhi, 1999.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Walaa Nabil Taha Fasfous This is me 0000-0002-5446-4367

Rajat Nath 0000-0003-4766-6523

Reza Sharafdini This is me 0000-0002-3171-2209

Publication Date December 8, 2020
Published in Issue Year 2020 Volume: 49 Issue: 6

Cite

APA Fasfous, W. N. T., Nath, R., & Sharafdini, R. (2020). Various spectra and energies of commuting graphs of finite rings. Hacettepe Journal of Mathematics and Statistics, 49(6), 1915-1925. https://doi.org/10.15672/hujms.540309
AMA Fasfous WNT, Nath R, Sharafdini R. Various spectra and energies of commuting graphs of finite rings. Hacettepe Journal of Mathematics and Statistics. December 2020;49(6):1915-1925. doi:10.15672/hujms.540309
Chicago Fasfous, Walaa Nabil Taha, Rajat Nath, and Reza Sharafdini. “Various Spectra and Energies of Commuting Graphs of Finite Rings”. Hacettepe Journal of Mathematics and Statistics 49, no. 6 (December 2020): 1915-25. https://doi.org/10.15672/hujms.540309.
EndNote Fasfous WNT, Nath R, Sharafdini R (December 1, 2020) Various spectra and energies of commuting graphs of finite rings. Hacettepe Journal of Mathematics and Statistics 49 6 1915–1925.
IEEE W. N. T. Fasfous, R. Nath, and R. Sharafdini, “Various spectra and energies of commuting graphs of finite rings”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 6, pp. 1915–1925, 2020, doi: 10.15672/hujms.540309.
ISNAD Fasfous, Walaa Nabil Taha et al. “Various Spectra and Energies of Commuting Graphs of Finite Rings”. Hacettepe Journal of Mathematics and Statistics 49/6 (December 2020), 1915-1925. https://doi.org/10.15672/hujms.540309.
JAMA Fasfous WNT, Nath R, Sharafdini R. Various spectra and energies of commuting graphs of finite rings. Hacettepe Journal of Mathematics and Statistics. 2020;49:1915–1925.
MLA Fasfous, Walaa Nabil Taha et al. “Various Spectra and Energies of Commuting Graphs of Finite Rings”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 6, 2020, pp. 1915-2, doi:10.15672/hujms.540309.
Vancouver Fasfous WNT, Nath R, Sharafdini R. Various spectra and energies of commuting graphs of finite rings. Hacettepe Journal of Mathematics and Statistics. 2020;49(6):1915-2.