Various spectra and energies of commuting graphs of finite rings

Walaa Nabil Taha Fasfous; Rajat Nath; Reza Sharafdini

doi:10.15672/hujms.540309

Araştırma Makalesi

Yıl 2020, Cilt: 49 Sayı: 6, 1915 - 1925, 08.12.2020

Walaa Nabil Taha Fasfous Rajat Nath , Reza Sharafdini

https://doi.org/10.15672/hujms.540309

Cited By: 7

Öz

Kaynakça

[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

Yıl 2020, Cilt: 49 Sayı: 6, 1915 - 1925, 08.12.2020

Walaa Nabil Taha Fasfous Rajat Nath , Reza Sharafdini

https://doi.org/10.15672/hujms.540309

Cited By: 7

Öz

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.

Anahtar Kelimeler

commuting graph, spectrum, energy, finite ring

Kaynakça

[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.

Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Matematik
Yazarlar	Walaa Nabil Taha Fasfous Bu kişi benim 0000-0002-5446-4367 Rajat Nath 0000-0003-4766-6523 Reza Sharafdini Bu kişi benim 0000-0002-3171-2209
Yayımlanma Tarihi	8 Aralık 2020
Yayımlandığı Sayı	Yıl 2020 Cilt: 49 Sayı: 6

Kaynak Göster

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. Aralık 2020;49(6):1915-1925. doi:10.15672/hujms.540309
Chicago	Fasfous, Walaa Nabil Taha, Rajat Nath, ve Reza Sharafdini. “Various Spectra and Energies of Commuting Graphs of Finite Rings”. Hacettepe Journal of Mathematics and Statistics 49, sy. 6 (Aralık 2020): 1915-25. https://doi.org/10.15672/hujms.540309.
EndNote	Fasfous WNT, Nath R, Sharafdini R (01 Aralık 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, ve R. Sharafdini, “Various spectra and energies of commuting graphs of finite rings”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 6, ss. 1915–1925, 2020, doi: 10.15672/hujms.540309.
ISNAD	Fasfous, Walaa Nabil Taha vd. “Various Spectra and Energies of Commuting Graphs of Finite Rings”. Hacettepe Journal of Mathematics and Statistics 49/6 (Aralık 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 vd. “Various Spectra and Energies of Commuting Graphs of Finite Rings”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 6, 2020, ss. 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.