Weighted topological indices of graphs

Raza, Zahid; Rather, Bilal Ahmad; Ghorbani, Modjtaba

doi:10.22049/cco.2024.29895.2211

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	Weighted topological indices of graphs
Communications in Combinatorics and Optimization
مقاله 19، دوره 11، شماره 2، شهریور 2026، صفحه 643-659 اصل مقاله (448.21 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2024.29895.2211
نویسندگان
Zahid Raza¹؛ Bilal Ahmad Rather¹^{، 2}؛ Modjtaba Ghorbani^* ³
¹Department of Mathematics, College of Sciences, University of Sharjah, UAE
²Department of Applied Mathematics, School of Engineering, Samarkand International University of Technology, Samarkand 140100, Uzbekistan
³Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-163, I. R. Iran
چکیده
The definition of the weighted topological index associated with a degree function $\phi$ is $\Phi(G)=\sum_{uv\in E(G)}\phi(d_{u},d_{v})$, where $d_{u}$ denotes the degree of node $u$ and $\phi$ satisfies symmetric property $\phi(d_{u},d_{v})=\phi(d_{v},d_{u})$. In this paper, we characterized extremal graphs and presented several results concerning the function $\Phi(G)$ in terms of various graph invariants. Additionally, we characterize the graphs that achieve these bounds and present multiple bounds for $\Phi(G)$ for the class of cozero divisor graphs defined on commutative rings.
کلیدواژه‌ها
topological index؛ inequalities؛ extremal graphs؛ cozero divisor graphs

مراجع
[1] M. Afkhami and K. Khashyarmanesh, The cozero divisor graph of a commutative ring., Southeast Asian Bull. Math. 35 (2011), no. 5, 753–762. [2] M. Afkhami and K. Khashyarmanesh, On the cozero-divisor graphs of commutative rings and their comple-ments., Bull. Malays. Math. Sci. Soc. 35 (2012), no. 4, 935–944. [3] M. Afkhami and K. Khashyarmanesh, Planar, outerplanar, and ring graph of the cozero-divisor graph of a finite commutative ring, J. Algebra Appl. 11 (2012), no. 6, Artile ID: 1250103. https://doi.org/10.1142/S0219498812501034 [4] M. Afkhami and K. Khashyarmanesh, On the cozero-divisor graphs and comaximal graphs of commutative rings, J. Algebra Appl. 12 (2013), no. 3, Artile ID: 1250173. https://doi.org/10.1142/S0219498812501733 [5] S. Akbari, F. Alizadeh, and S. Khojasteh, Some results on cozero-divisor graph of a commutative ring, J. Algebra Appl. 13 (2014), no. 3, Artile ID: 1350113. https://doi.org/10.1142/S0219498813501132 [6] S. Akbari and S. Khojasteh, Commutative rings whose cozero-divisor graphs are unicyclic or of bounded degree, Comm. Algebra 42 (2014), no. 4, 1594–1605. https://doi.org/10.1080/00927872.2012.745867 [7] M. Bakhtyiari, R. Nikandish, and M.J. Nikmehr, Coloring of cozero-divisor graphs of commutative von Neumann regular rings, Proc. Math. Sci. 130 (2020), no. 1, Article number: 49 https://doi.org/10.1007/s12044-020-00569-5 [8] G. Chartrand and P. Zhang, Introduction to Graph Theory, McGraw-Hill Higher Education, New Delhi, 2005. [9] X. Chen, On ABC eigenvalues and ABC energy, Linear Algebra Appl. 544 (2018), 141–157. https://doi.org/10.1016/j.laa.2018.01.011 [10] K.C. Das, I. Gutman, I. Milovanović, E. Milovanović, and B. Furtula, Degree-based energies of graphs, Linear Algebra Appl. 554 (2018), 185–204. https://doi.org/10.1016/j.laa.2018.05.027 [11] I. Gutman, Degree-based topological indices, Croat. Chem. Acta. 86 (2013), no. 4, 351–361. http://doi.org/10.5562/cca2294 [12] I. Gutman, Relating graph energy with vertex-degree-based energies, Vojnoteh. Glas. 68 (2020), no. 4, 715–725. [13] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), no. 1, 11–16. [14] I Gutman, J. Monsalve, and J. Rada, A relation between a vertex-degree-based topological index and its energy, Linear Algebra Appl. 636 (2022), 134–142. https://doi.org/10.1016/j.laa.2021.11.021 [15] Z. Hu, X. Li, and D. Peng, Graphs with minimum vertex-degree function-index for convex functions, MATCH Commun. Math. Comput. Chem. 88 (2022), no. 3, 521–533. https://doi.org/10.46793/match.88-3.521H [16] V.R. Kulli and I. Gutman, Computation of sombor indices of certain networks, SSRG Int. J. Appl. Chem. 8 (2021), no. 1, 1–5. https://doi.org/10.14445/23939133/IJAC-V8I1P101 [17] X. Li, Y. Li, and J. Song, The asymptotic value of graph energy for random graphs with degree-based weights, Discrete Appl. Math. 284 (2020), 481–488. https://doi.org/10.1016/j.dam.2020.04.008 [18] X. Li, Y. Li, and Z. Wang, The asymptotic value of energy for matrices with degree-distance-based entries of random graphs, Linear Algebra Appl. 603 (2020), 390–401. https://doi.org/10.1016/j.laa.2020.06.020 [19] X. Li, Y. Li, and Z. Wang, Asymptotic values of four Laplacian-type energies for matrices with degree-distance-based entries of random graphs, Linear Algebra Appl. 612 (2021), 318–333. https://doi.org/10.1016/j.laa.2020.11.005 [20] X. Li and D. Peng, Extremal problems for graphical function-indices and fweighted adjacency matrix, Discrete Math. Lett 9 (2022), 57–66. [21] X. Li and Z. Wang, Trees with extremal spectral radius of weighted adjacency matrices among trees weighted by degree-based indices, Linear Algebra Appl. 620 (2021), 61–75. https://doi.org/10.1016/j.laa.2021.02.023 [22] R. Liu and W.C. Shiu, General Randić matrix and general Randić incidence matrix, Discrete Appl. Math. 186 (2015), 168–175. https://doi.org/10.1016/j.dam.2015.01.029 [23] P. Mathil, B. Baloda, and J. Kumar, On the cozero-divisor graphs associated to rings, AKCE Int. J. Graphs Comb. 19 (2022), no. 3, 238–248. https://doi.org/10.1080/09728600.2022.2111241 [24] R. Nikandish, M.J. Nikmehr, and M. Bakhtyiari, Metric and strong metric dimension in cozero-divisor graphs, Mediterr. J. Math. 18 (2021), no. 3, Article number: 112. https://doi.org/10.1007/s00009-021-01772-y [25] M. Randić, On characterization of molecular branching, J. Am. Chem. Soc. 97 (1975), 6609–6615. [26] M. Randić, Generalized molecular descriptors, J. Math. Chem. 7 (1991), no. 1, 155–168. https://doi.org/10.1007/BF01200821 [27] M. Randić, Topological indices, Encyclopedia of Computational Chemistry, P. von Rague Schleyer, Editor-in-Chief, London: Wiley (1998), 3018–3032. [28] B.A. Rather and M. Imran, Sharp bounds on the sombor energy of graphs, MATCH Commun. Math. Comput. Chem. 88 (2022), no. 3, 605–624. https://doi.org/10.46793/match.88-3.605R [29] B.A. Rather, M. Imran, and S. Pirzada, Sombor index and eigenvalues of comaximal graphs of commutative rings, J. Algebra Appl. 23 (2024), no. 6, Article ID: 2450115. https://doi.org/10.1142/S0219498824501159 [30] Z. Raza, B. Rather, and M. Ghorbani, On cozero divisor graphs of ring $\mathbb{Z}_n$, Commun. Comb. Optim. (2024), https://doi.org/10.22049/cco.2024.26112.1974 [31] V.S. Shegehalli and R. Kanabur, Arithmetic-geometric indices of path graph, J. Math. Comput. Sci 6 (2015), no. 1, 19–24. [32] M. Young, Adjacency matrices of zero-divisor graphs of integers modulo n, Involve 8 (2015), no. 5, 753–761. https://doi.org/10.2140/involve.2015.8.753 [33] L. Zheng, G.X. Tian, and S.Y. Cui, Arithmetic–geometric energy of specific graphs, Discrete Math. Algorithms Appl. 13 (2021), no. 2, Artile ID: 2150005. https://doi.org/10.1142/S1793830921500051
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Weighted topological indices of graphs