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The forgotten index of hypergraphs and some hypergraph operations | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 شهریور 1404 اصل مقاله (439.25 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30434.2466 | ||
| نویسندگان | ||
| Shashwath S Shetty؛ K Arathi Bhat* | ||
| Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, 576104, Karnataka, India | ||
| چکیده | ||
| Hypergraphs generalize traditional graphs by allowing edges to connect more than two vertices, enabling a richer representation of relationships in complex systems. Forgotten topological index, or simply $F$-index of a hypergraph, is defined as the sum of cubes of the degrees of all the vertices of the hypergraph. Initially, some sharp bounds for the $F$-index of hypergraphs in terms of other degree-based topological indices have been obtained. A minimally connected hypergraph is a connected hypergraph such that the removal of any hyperedge disconnects the hypergraph. We have characterized the extremal minimally connected hypergraphs corresponding to the $F$-index among minimally connected hypergraphs on $n$ vertices. The hyperstar and hyperpath with minimum and maximum $F$-indices have been studied. The upper and lower bounds for the $F$-index of the hypergraphs and bipartite hypergraphs are also given. We conclude this article by computing the $F$-index of join, corona product, and Cartesian product of two hypergraphs. | ||
| کلیدواژه‌ها | ||
| Hyperstar؛ hyperpath؛ sunflower؛ Cartesian product؛ corona | ||
| مراجع | ||
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[1] S. Akhter and M. Imran, Computing the forgotten topological index of four operations on graphs, AKCE Int. J. Graphs Comb. 14 (2017), no. 1, 70–79. https://doi.org/10.1016/j.akcej.2016.11.012
[2] D. Arya and M. Worring, Exploiting relational information in social networks using geometric deep learning on hypergraphs, Proceedings of the 2018 ACM on International Conference on Multimedia Retrieval (New York, NY, USA), Association for Computing Machinery, 2018, pp. 117–125.
[3] S. Ashraf, M. Imran, S.A.U.H. Bokhary, and S. Akhter, The Wiener index, degree distance index and Gutman index of composite hypergraphs and sunflower hypergraphs, Heliyon 8 (2022), no. 12, e12382. https://doi.org/10.1016/j.heliyon.2022.e12382
[4] C. Berge, Hypergraphs: Combinatorics of Finite Sets, vol. 45, Elsevier, 1984.
[5] Z. Che and Z. Chen, Lower and upper bounds of the forgotten topological index, MATCH Commun. Math. Comput. Chem 76 (2016), no. 3, 635–648.
[6] B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015), no. 4, 1184–1190. https://doi.org/10.1007/s10910-015-0480-z
[7] B. Furtula, I. Gutman, and M. Dehmer, On structure-sensitivity of degree-based topological indices, Appl. Math. Comput. 219 (2013), no. 17, 8973–8978. https://doi.org/10.1016/j.amc.2013.03.072
[8] W. Gao, M.R. Farahani, and L. Shi, Forgotten topological index of some drug structures, Acta Med. Mediterr. 32 (2016), no. 1, 579–585.
[9] W. Gao, M.K. Siddiqui, M. Imran, M.K. Jamil, and M.R. Farahani, Forgotten topological index of chemical structure in drugs, Saudi Pharm. J. 24 (2016), no. 3, 258–264. https://doi.org/10.1016/j.jsps.2016.04.012
[10] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total $\pi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538. https://doi.org/10.1016/0009-2614(72)85099-1
[11] E.V. Konstantinova and V.A. Skorobogatov, Application of hypergraph theory in chemistry, Discrete Math. 235 (2001), no. 1-3, 365–383. https://doi.org/10.1016/S0012-365X(00)00290-9
[12] G. Lee, M. Choe, and K. Shin, How do hyperedges overlap in real-world hypergraphs-patterns, measures, and generators, Proceedings of the Web Conference 2021 (New York, NY, USA), Association for Computing Machinery, 2021, pp. 3396–3407. [13] K.A. Murgas, E. Saucan, and R. Sandhu, Hypergraph geometry reflects higher-order dynamics in protein interaction networks, Sci. Rep. 12 (2022), no. 1, 20879. https://doi.org/10.1038/s41598-022-24584-w
[14] J.A. Rodrıguez, On the Wiener index and the eccentric distance sum of hypergraphs, MATCH Commun. Math. Comput. Chem. 54 (2005), no. 1, 209–220.
[15] S.S. Shetty and K. A. Bhat, Sombor index of hypergraphs, MATCH Commun. Math. Comput. Chem. 91 (2024), no. 1, 235–254. https://doi.org/10.46793/match.91-1.235S
[16] S.S. Shetty and K.A. Bhat, On the first Zagreb index of graphs with self-loops, AKCE int. j. graphs comb. 20 (2023), no. 3, 326–331. https://doi.org/10.1080/09728600.2023.2246515
[17] G.H. Shirdel, A. Mortezaee, and L. Alameri, General Randić index of uniform hypergraphs, Iranian J. Math. Chem. 14 (2023), no. 2, 121–133. https://doi.org/10.22052/IJMC.2023.252836.1712
[18] L. Sun, J. Wu, H. Cai, and Z. Luo, The Wiener index of r-uniform hypergraphs, Bull. Malays. Math. Sci. Soc. 40 (2017), no. 3, 1093–1113. https://doi.org/10.1007/s40840-016-0359-6
[19] T. Vetr´ık, Degree-based indices of hypergraphs: Definitions and first results, Asian-Eur. J. Math. 17 (2024), no. 4, 2450023. https://doi.org/10.1142/S1793557124500232
[20] D.B. West, Introduction to Graph Theory, vol. 2, Prentice Hall, Upper Saddle River, 2001. | ||
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آمار تعداد مشاهده مقاله: 59 تعداد دریافت فایل اصل مقاله: 47 |
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