Genus of commuting graphs of some classes of finite rings
Abstract
In this paper, we compute the genus of commuting graphs of non-commutative rings of order p4, p5, p2q and p3q, where p and q are prime integers. We also characterize those finite rings such that their commuting graphs are planar or toroidal.
Downloads
References
Abdollahi, A. Commuting graphs of full matrix rings over finite fields, Linear Algebra Appl. 428(11-12), 2947–2954, (2008).
Akbari, S., Ghandehari, M., Hadian, M. and Mohammadian, A. On commuting graphs of semisimple rings, Linear Algebra Appl. 390, 345–355, (2004).
Battle, J., Harary, F., Kodama, Y. and Youngs, J. W. T. Additivity of the genus of a graph, Bull. Amer. Math. Soc. 68(6), 565–568, (1962).
Brauer, R. and Fowler, K. A. On groups of even order, Ann. Math. 62(2), 565–583, (1955).
Dutta, J., Fasfous, W. N. T. and Nath, R. K. Spectrum and genus of commuting graphs of some classes of finite rings, Acta Comment. Univ. Tartu. Math. 23(1), 5–12, (2019).
Fasfous, W. N. T. and Nath, R. K. Common neighborhood spectrum and energy of commuting graphs of finite rings, Palest. J. Math. accepted for publication, (2023).
Fasfous, W. N. T., Nath, R. K. and Sharafdini, R. Various spectra and energies of commuting graphs of finite rings, Hacet. J. Math. Stat. 49(6), 1915–1925, (2020).
Mohammadian, A. On commuting graphs of finite matrix rings, Comm. Algebra 38(3), 988–994, (2010).
Nath, R. K. A note on super integral rings, Bol. Soc. Parana. Mat. 38(4), 213–218, (2020).
Omidi, G. R. and Vatandoost, E. On the commuting graph of rings, J. Algebra Appl. 10(3), 521–527, (2011).
Vatandoost, E., Ramezani, F. and Bahraini, A. On the commuting graph of non-commutative rings of order pnq, J. Linear Topological Algebra 3(1), 1–6, (2014).
Vatandoost, E. and Ramezani, F. On the commuting graph of some non-commutative rings with unity, J. Linear Topological Algebra 5(4), 289–294, (2016).
White, A. T. Graphs, Groups and Surfaces, North-Holland Mathematics Studies 8, American Elsevier Publishing Co. New York, 1973.
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
