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On some topological indices over rectangular grids | ||
| Journal of Hyperstructures | ||
| دوره 12، شماره 2، 2023، صفحه 322-335 اصل مقاله (323.9 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2023.2806 | ||
| نویسندگان | ||
| Hadi Parsian* 1؛ Ali Parsian2 | ||
| 1Department of Civil Engineering, Faculty of Civil Engineering, Art and Architecture, WTIAU, Tehran, Iran. | ||
| 2Department of Mathematics, Tafresh University, Tafresh 39518 79611, Iran | ||
| چکیده | ||
| A topological index is a real number related to a graph,which is considered as a structural invariant. Some examples are Sombor index, Randi´c index, Zagreb indices, and Harmonic index.In the present paper, we consider the function Ind from the set of all rectangular grids to the set of real numbers, which assigns to each rectangular grid, one of its above indices. Then we show that the only non-degenerate indices over retangular grids, are Sombor index and Randi´c index, while Zagreb indices and the Harmonic index are degenerate. In the following, we determine rectangular grids with fixed diameter d, where maximum and minimum of the above indices occures on them, in the case m ≥ 3, n ≥ 3. Finally, we find the amounts of these indices. | ||
| کلیدواژه‌ها | ||
| Graph؛ Graphical indices؛ Isomorphism | ||
| مراجع | ||
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[1] A. Alidadi, A. Parsian and H. Arianpoor, The minimum Sombor index for uni-cyclic graphs with fixed diameter, MATCH Commun. Math. Comput. Chem., 88(2022), 561–572. [2] M. F. Ashby, The properties of foams and lattices, Philos. Transact. A Math.Phys. Eng. Sci., 364 (2005), 15–30. [3] K. C. Das, A. S. C¸ evik, I. N. Cangul, and Y. Shang, On Sombor index, Symmetry,13 (2021), 1–12. [4] H. Deng, S. Balachandran, S. K. Ayyaswamy, and Y. B. Venkatakrishnan, On the harmonic index and the chromatic number of a graph, Discret. Appl. Math.,161 (2013), 2740–2744. [5] S. Fajtlowicz, On conjectures of Graffiti-II, Congr. Numer., 60 (1987), 187–197. [6] I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem., 50 (2004), 83–92. [7] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem., 86 (2021), 11–16. [8] I. Gutman, Some basic properties of Sombor indices, Open J. Discret. Appl.Math., 4 (2021), 1-3. [9] I. Gutman, B. Ruˇsˇci´c, N. Trinajsti´c, J. L. Wilcox, Jr., Graph theory and molecular orbitals. XII. Acyclic polyenes, J. Chem. Phys., 62 (9) (1975), 3399–3405. [10] I. Gutman and N. Trinajsti´c, Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17 (1972), 535–538. [11] F. Harary, Graph Theory, New Delhi: Narosa Publishing House (1998). [12] Y. Hu, X. Li, Y. Shi, T. Xu and I. Gutman, On molecular graphs with small-est and greatest zeroth order general Randi´c index, MATCH Commun. Math.Comput. Chem., 54 (2005), 425–434. [13] L. B. Kier and L. H. Hall, Molecular Connectivity in Chemistry and Drug Re-search, New York: Academic Press (1976). [14] L. B. Kier and L. H. Hall, Molecular Connectivity in Structure Activity Analysis,New York: Wiley (1986). [15] X. Li and Y. Shi, A survey on the Randi´c index, MATCH Commun. Math.Comput. Chem., 59 (2008), 127–156. [16] B. Liu and I. Gutman, On general Randi´c indices, MATCH Commun. Math.Comput. Chem., 58 (2007), 147–154. [17] B. Liu and Z. You, A survey on comparing Zagreb indices, MATCH Commun.Math. Comput. Chem., 65 (2011), 581–593. [18] S. Nikoli´c, G. Kovaˇcevi´c, A. Miliˇcevi´c, and N. Trinajsti´c, The Zagreb indices 30 years after, Croat. Chem. Acta., 76 (2003), 113–124. [19] I. Niven, H. S. Zuckerman, and H. L. Montgomery, An Introduction to the Theory of Numbers, New York: Wiley (1991). [20] B. N. Onagh, The harmonic index of subdivision graphs, Trans. Comb., 6 (2017),15–27. [21] M. Randi´c, M. Noviˇc, and D. Plavˇsi´c, Solved and unsolved problems in structural chemistry, Boca Raton: CRC Press (2016). [22] C. Pan, Y. Han and J. Lu, Design and optimization of lattice structures: a review, Appl. Sci., 10 (2020), 63–74. [23] H. S. Ramane, I. Gutman, K. Bhajantri, and D. V. Kitturmath, Sombor index of some graph transformations, Commun. Comb. Optim., 8 (2023), 193–205. [24] M. Randi´c, On characterization of molecular branching, J. Am. Chem. Soc., 97 (1975), 6609–6615. [25] M. Randi´c, On history of the Randi´c index and emerging hostility toward chemical graph theory, MATCH Commun. Math. Comput. Chem., 59 (2008), 5-124. [26] M. Randi´c, The connectivity index 25 years after, J. Mol. Graph. Model., 20 (2001), 19–35. [27] R. Todeschini, V. Consonni, Handbook of Molecular Descriptors, New York:Wiley-VCH (2000). [28] X. Xu, Relationships between harmonic index and other topological indices, Appl.Math. Sci., 6 (2012), 2013–2018. [29] C. Yan, L. Hao, A. Hussein, S. L. Bubb, P. Young, and D. Raymont, Evaluation of light-weight AlSi10Mg periodic cellular lattice structures fabricated via direct metal laser sintering, J. Mater. Process. Technol., 214 (2014), 856–864. [30] L. Zhong, The harmonic index for graphs, Appl. Math. Lett., 25 (2012), 561–566. [31] L. Zhong, The harmonic index on unicyclic graphs, Ars Comb., 104 (2012),261–269. [32] L. Zhong and K. Xu, The harmonic index for bicyclic graphs, Util. Math., 90(2013), 23–32 | ||
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