Weighted topological indices of graphs

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

doi:10.22049/cco.2024.29895.2211

تعداد نشریات	6
تعداد شماره‌ها	123
تعداد مقالات	1,578
تعداد مشاهده مقاله	1,707,577
تعداد دریافت فایل اصل مقاله	1,590,901

	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
آمار تعداد مشاهده مقاله: 508 تعداد دریافت فایل اصل مقاله: 761

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Weighted topological indices of graphs