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Some inequalities of reformulated and entire Inf-Sombor index | ||
Journal of Hyperstructures | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 10 خرداد 1404 اصل مقاله (2.43 M) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22098/jhs.2025.16439.1067 | ||
نویسندگان | ||
Jalappa Meti* 1؛ Manohar S H2؛ Boregowda H S3 | ||
1Department of Studies and Research in Mathematics, Tumkur University, Tumakuru, India | ||
2Department of Studies and Research in Mathematics, Tumkur University, Jnanasiri campus, Bidarakatte, India | ||
3Department of Studies and Research in Mathematics, Tumkur University, Jnanasiri campus, Bidarakatte, India. | ||
چکیده | ||
The concept of the Sombor index was extended by Reti et. al. [1] by introducing a pSombor index which can be seen as the p norm of the vector x = (d(u), d(v)) as p → ∞, ∥x∥∞ = max{d(u), d(v)}. Inspired by this, we defined indices namely, Reformulated Inf- Sombor index, Entire Inf-Sombor index, and KG Inf-Sombor index. Also, we present lower and upper bounds by using some graph parameters and obtain exact values of these new topological indices in some graph families. Further, we evaluated the statistical behavior of these indices after computing index values for different types of dendrimers for various growth values k. | ||
کلیدواژهها | ||
Platt number؛ Inf Sombor index؛ Reformulated Inf Sombor index؛ Entire Inf Sombor index | ||
مراجع | ||
[1] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Communications in Mathematical and in Computer Chemistry, 86 (2021), 11-16. [2] T. Réti, T. Došlic, and A. Ali, On the Sombor index of graphs, Contributions to Mathematics, 3 (2021), 11-18. [3] J. L. Gross, J. Yellen and M. Anderson, Graph theory and its applications Chapman and Hall/CRC, 2018. [4] P. Zhang and G. Chartrand, Introduction to graph theory, 2 Tata McGraw-Hill, New York, 2006. [5] I. Gutman, and K. C. Das, The first Zagreb index 30 years after, MATCH-Communications in Mathematical and in Computer Chemistry, 50 (2004), 83-92. [6] I. Gutman, and N. Trinajstić, Graph theory and molecular orbitals. Total phi-electron energy of alternate hydrocarbons, Chemical physics letters, 17 (1972), 535-538. [7] B. Zhou, Zagreb indices, MATCH-Communications in Mathematical and in Computer Chemistry 52 (2004), 113-118. [8] B. Furtula and I. Gutman, A forgotten topological index, Journal of mathematical chemistry, 53 (2015), 1184-1190. [9] C. Zhongyuan and C. Zhibo, Lower and upper bounds of the forgotten topological index, MATCH Communications in Mathematical and in Computer Chemistry, 76 (2016), 635-648. [10] L. Xueliang and Y. Shi, A survey on the Randic index, MATCH Communications in Mathematical and in Computer Chemistry, 59 (2008), 127-156. [11] M. Randic, Characterization of molecular branching, Journal of the American Chemical Society, 97 (1975), 6609-6615. [12] J. A. Méndez-Bermúdez, R. Aguilar-Sanchez, E. D. Molina, J. M. Rodríguez Mean sombor index, arXiv preprint, (2021). [13] J. R. Platt Prediction of isomeric differences in paraffin properties, The Journal of Physical Chemistry, 56 (1952), 328-336. [14] M. M. Belavadi and T. A. Mangam, Platt number of total graphs, International Journal of Applied Mathematics, 31 (2018), 593. [15] A. Akbar and D. Dimitrov, On the extremal graphs with respect to bond incident degree indices, Discrete Applied Mathematics, 238 (2018), 32-40. [16] I. Gutman and E. Estrada, Topological indices based on the line graph of the molecular graph, Journal of chemical information and computer sciences, 36 (1996), 541-543. [17] A. Saleh, and I. N. Cangul, On the entire Randic index of graphs, Advances in Applied Mathematics, 20 (2021), 1559-1569. [18] F. Movahedi and M. H. Akhbari Entire Sombor index of graphs, Iranian Journal of Mathematical Chemistry, 14 (2023), 33-45. [19] N. Harish and B. Chaluvaraju, Some Inequalities for the Entire Sombor Index, International journal of mathematical combinatorics, 1 (2024), 50-64. [20] N. Harish, B. Sarveshkumar and B. Chaluvaraju, The reformulated Sombor index of a graph, Transactions on Combinatorics, 13 (2024), 1-16. [21] A. Miličević, S. Nikolić and N. Trinajstić, On reformulated Zagreb indices, Molecular diversity, 8 (2004), 393-399. [22] V. R. Kulli, N. Harish, B. Chaluvaraju, I. Gutman, Mathematical properties of KG Sombor index, Bulletin of International Mathematical Virtual Institute, 12 (2022), 379-386. [23] A. Alwardi, A. Alqesmah, R. Rangarajan and I. N. Cangul, Entire Zagreb indices of graphs, Discrete mathematics, algorithms and applications, 10 (2018), 1850037. [24] I. Gutman, V. R. Kulli, B. Chaluvaraju and H. S. Boregowda, On Banhatti and Zagreb indices, Journal of International Mathematical Virtual Institute, 7 (2017), 53-67. [25] V. R. Kulli, B. Chaluvaraju and H. S. Boregowda, The hyper-Zagreb index of some derived graphs, International Journal of Mathematical Archive, 9 (2018), 124-129. [26] H. S. Boregowda, Topological indices of some derived graphs through M-Polynomials, Advances and Applications in Mathematical Sciences, (2022). [27] H. S. Boregowda, Wiener Type Indices Of Certain Classes of Trees, South East Asian Journal of Mathematics and Mathematical Sciences, 17 (2021), 241-250. [28] V. R. Kulli, B. Chaluvaraju and H. S. Boregowda, Some degree based connectivity indices of Kulli cycle windmill graphs, South Asian Journal of Mathematics, 6 (2016), 263-268. [29] H. Marzieh, Study of inverse sum indeg index, Journal of Nanoscience and Nanotechnology, 7 (2017), 103-109. [30] B. Klajnert and B. Maria, Dendrimers: properties and applications, Acta biochimica polonica, 48 (2001), 199-208. [31] A. R. Ashrafi and M. Mirzargar, PI, Szeged and edge Szeged indices of an infinite family of nanostar dendrimers, Indian Journal of Chemistry, 47 (2008), 538-541. [32] Ü. Şener and B. Şahin Total domination number of regular dendrimer graph, Turkish Journal of Mathematics and Computer Science, 11 (2019), 81-84. [33] V. Mathad, P. Padmapriya and M. A. Sangamesha, Some topological indices of phosphorus containing dendrimers, Palestine Journal of Mathematics, 10 (2021), 151–160. [34] V. R. Kulli, B. Chaluvaraju and H. S. Boregowda, Some bounds of sum connectivity Banhatti index of graphs, Palestine Journal of Mathematics, 8 (2019), 355-364. [35] I. Sarkar, N. Manjunath, B. Chaluvaraju and V. Lokesha Bounds of Sombor Index for F-Sum Operation, Palestine Journal of Mathematics, 12 (2023), 504-516. [36] A. Jahanbani, The Multiplicative Hyper-Zagreb index of Graph Operations, Palestine Journal of Mathematics, 9 (2020), 82-96. [37] V. Lokesha, S. Jain, M. Muddalapuram, A. S. Çevik and I. N. Cangül, Bounds for the sum of cubes of vertex degrees of splice graphs, TWMS Journal Of Applied And Engineering Mathematics, 10 (2020), 741-750. [38] P. S. Ranjini, V. Lokesha and S. Kumar, The K. Banhatti Indices of Certain Graphs, Southeast Asian Bulletin of Mathematics, 46 (2022), 453. [39] v. Lokesha, P. S. Ranjini and M. R. Harini, Limits for the Some Topological Indices of Vertex Corona Graph, International Journal of Mathematical Combinatorics, 4 (2024), 42. [40] A. S. Maragadam, K. Nirupadi, D. Dafik, V. Lokesha, M. Manjunath and I. H. Agustin, Neighborhood vertex corona product of graphs in a semi-total point graph, AIP Conference Proceedings, 3176 (2024). [41] S. Jain, A. S. Maragadam, V. Lokesha, Topological Aspects of Synthetic Polymers through NM Polynomials, 2nd International Conference on Neural Networks and Machine Learning, (2023). | ||
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