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Some of the graph energies of zero-divisor graphs of finite commutative rings | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 19، دوره 14، شماره 7، مهر 2023، صفحه 207-216 اصل مقاله (362.61 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.7136 | ||
| نویسندگان | ||
| Sharife Chokani؛ Fateme Movahedi* ؛ Seyyed Mostafa Taheri | ||
| Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran | ||
| تاریخ دریافت: 21 اسفند 1400، تاریخ بازنگری: 14 مرداد 1401، تاریخ پذیرش: 22 شهریور 1401 | ||
| چکیده | ||
| In this paper, we investigate some of the graph energies of the zero-divisor graph $\Gamma(R)$ of finite commutative rings $R$. Let $Z(R)$ be the set of zero-divisors of a commutative ring $R$ with non-zero identity and $Z^*(R)=Z(R)\setminus \{0\}$. The zero-divisor graph of $R$, denoted by $\Gamma(R)$, is a simple graph whose vertex set in $Z^*(R)$ and two vertices $u$ and $v$ are adjacent if and only if $uv=vu=0$. We investigate some energies of $\Gamma(R)$ for the commutative rings $R\simeq \mathbb{Z}_{p^2}\times \mathbb{Z}_{q}$, $R\simeq \mathbb{Z}_{p}\times \mathbb{Z}_{p}\times \mathbb{Z}_{p}$ and $R\simeq \mathbb{Z}_{p}\times \mathbb{Z}_{p}\times \mathbb{Z}_{p}\times \mathbb{Z}_{p}$ where $p, q$ the prime numbers. | ||
| کلیدواژه‌ها | ||
| Commutative ring؛ Zero-divisor graph؛ Line graph؛ Minimum edge dominating energy؛ Laplacian energy | ||
| مراجع | ||
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[1] N. Abreu, D. M. Cardoso, I. Gutman, E. A. Martins and M. Robbiano, Bounds for the signless Laplacian energy, Linear Alg. Appl. 435 (2011), no. 10, 2365–2374. [2] A. Ahmad, R. Hasni, N. Akhter and K. Elahi, Analysis of distance-based topological polynomials associated with zero-divisor graphs, Comput. Mater. Continua Henderson 70 (2022), no. 2, 2895–2904. [3] M. H. Akhbari, K. K. Choong and F. Movahedi, A note on the minimum edge dominating energy of graphs, J. Appl. Math. Comput. 63 (2020), 295–310. [4] D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 167 (1999), 434–447. [5] S. Arumugam and S. Velammal, Edge Domination in Graphs, Taiwanese J. Math. 2 (1998), no. 2, 173–179. [6] S. B. Bozkurt and D. Bozkurt, On Incidence Energy, MATCH Commun. Math. Comput. Chem. 72 (2014), 215–225. [7] S. Chokani, F. Movahedi and S.M. Taheri, Results on some energies of the Zero-divisor graph of the commutative ring Zn, 14th Iran. Int. Group Theory Conf., 2022, pp. 138–146. [8] D. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs, Theory and Application, Academic Press, New York, 1980. [9] K.C. Das and S.A. Mojallal, On Laplacian energy of graphs, Discrete Math. 325 (2014), 52–64. [10] K.C. Das and S.A. Mojallal, Relation between signless Laplacian energy of graph and its line graph, Linear Alg. Appl. 493 (2016), 91–107. [11] K.C. Das, S.A. Mojallal and I. Gutman, On energy of line graphs, Linear Alg. Appl. 499 (2016), 79–89. [12] R.P. Gupta, Independence and covering numbers of line graphs and total graphs. In: Harary, F. (ed.) Proof Techniques in Graph Theory, pp. 61-62, Academic Press, New York, 1969. [13] I. Gutman, The energy of a graph, Ber. Math-Statist. Sekt. Forschungsz. Graz 103 (1978), 1–22. [14] I. Gutman and B. Zhou, Laplacian energy of a graph, Linear Alg. Appl. 414 (2006), 29–37. [15] I. Gutman, M. Robbiano, E.A. Martins, D.M. Cardoso, L. Medina and O. Rojo, Energy of line graphs, Linear Alg. Appl. 433 (2010), 1312–1323. [16] I. Gutman, N. Trinajstic, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535–538. [17] F. Harary, Graph Theory, Addison-Wesley. Reading, 1972. [18] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker Inc., New York, 1998. [19] I.Z. Milovanoviic and E.I. Milovanoviic, Remarks on the energy and the minimum dominating energy of a graph, MATCH Commun. Math. Comput. Chem, 75 (2016), 305–314. [20] K. Monius, Eigenvalues of zero-divisor graphs of finite commutative rings, J. Alg. Combin. 54 (2021), 787–802. [21] F. Movahedi, The relation between the minimum edge dominating energy and the other energies, Discrete Math. Algorithms Appl. 12 (2020), no. 6, 2050078 (14 pages). [22] F. Movahedi, Bounds on the minimum edge dominating energy of induced subgraphs of a graph, Discrete Math. Algorithms Appl. 13 (2021), no. 06, 2150080. [23] F. Movahedi and M.H. Akhbari, New results on the minimum edge dominating energy of a graph, J. Math. Ext. 16 (2022), no. 5, 1–17. [24] N. Palanivel and A.V. Chithra, Signless Laplacian energy, distance Laplacian energy and distance signless Laplacian spectrum of unitary addition Cayley graphs, Linear Multilinear Alg. (2021), 1–22. doi.org/10.1080/03081087.2021.1996524 [25] M.R. Rajesh Kanna, B.N. Dharmendra and G. Sridhara, The minimum dominating energy of a graph, Int. J. Pure App. Math. 85 (2013), 707–718. [26] B.S. Reddy, R. Jain and N. Laxmikanth, Eigenvalues and Wiener index of the zero-divisor graph Γ(Zn), arXivpreprint arXiv:1707.05083 (2017). [27] M. Robbiano, R. Jimenez, Applications of a theorem by Ky Fan in the theory of Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. 62 (2009), 537–552. [28] S. Suthar and O. Prakash, Adjacency Matrix and Energy of the Line Graph of Γ(Zn), arXiv: Combinatorics (2018), arXiv:1806.08944. [29] B. Zhou, More on energy and Laplacian energy, MATCH Commun. Math. Comput. Chem. 64 (2010), 75–84. | ||
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