Research article

Extremal graphs and bounds for general Gutman index

  • Received: 12 June 2024 Revised: 25 September 2024 Accepted: 27 September 2024 Published: 25 October 2024
  • MSC : 05C09, 05C12, 05C35

  • In this paper, we solved some open problems on general Gutman index. More precisely, we characterized unicyclic graphs with extremal general Gutman index for some $ a $ and $ b $. We presented a sharp bound on general Gutman index of $ G $ in terms of order and vertex connectivity of $ G $. Also, we obtained some bounds on general Gutman index in terms of order, general Randić index, diameter, and independence number of graph $ G $. In addition, QSPR analysis on various anticancer drug structures was carried out to relate their physicochemical properties with the general Gutman index of the structure for some $ a $ and $ b $.

    Citation: Swathi Shetty, B. R. Rakshith, N. V. Sayinath Udupa. Extremal graphs and bounds for general Gutman index[J]. AIMS Mathematics, 2024, 9(11): 30454-30471. doi: 10.3934/math.20241470

    Related Papers:

  • In this paper, we solved some open problems on general Gutman index. More precisely, we characterized unicyclic graphs with extremal general Gutman index for some $ a $ and $ b $. We presented a sharp bound on general Gutman index of $ G $ in terms of order and vertex connectivity of $ G $. Also, we obtained some bounds on general Gutman index in terms of order, general Randić index, diameter, and independence number of graph $ G $. In addition, QSPR analysis on various anticancer drug structures was carried out to relate their physicochemical properties with the general Gutman index of the structure for some $ a $ and $ b $.



    加载中


    [1] A. Ali, B. Furtula, I. Redžepović, I. Gutman, Atom-bond sum-connectivity index, J. Math. Chem., 60 (2022), 2081–2093. https://doi.org/10.1007/s10910-022-01403-1 doi: 10.1007/s10910-022-01403-1
    [2] A. Alsinai, A. Saleh, H. Ahmed, L. N. Mishra, N. Soner, On fourth leap zagreb index of graphs, Discrete Math. Algorithms Appl., 15 (2023), 2250077. https://doi.org/10.1142/S179383092250077X doi: 10.1142/S179383092250077X
    [3] A. Altassan, B. A. Rather, M. Imran, Inverse sum indeg index (energy) with applications to anticancer drugs, Mathematics, 10 (2022), 4749. https://doi.org/10.3390/math10244749 doi: 10.3390/math10244749
    [4] V. Andova, D. Dimitrov, J. Fink, R. Skrekovski, Bounds on Gutman index, MATCH Commun. Math. Comput. Chem., 67 (2012), 515–524.
    [5] B. Bollobás, P. Erd$\ddot{o}$s, Graphs of extremal weights, Ars Combin., 50 (1998), 225–233.
    [6] X. Cheng, X. Li, Extremal general Gutman index of trees, MATCH Commun. Math. Comput. Chem., 89 (2023), 567–582. https://doi.org/10.46793/match.89-3.567C doi: 10.46793/match.89-3.567C
    [7] K. C. Das, G. Su, L. Xiong, Relation between degree distance and Gutman index of graphs, MATCH Commun. Math. Comput. Chem., 76 (2016), 221–232.
    [8] K. C. Das, T. Vetrík, General Gutman index of a graph, MATCH Commun. Math. Comput. Chem., 89 (2023), 583–603. https://doi.org/10.46793/match.89-3.583D doi: 10.46793/match.89-3.583D
    [9] L. Feng, The Gutman index of unicyclic graphs, Discrete Math. Algorithms Appl., 4 (2012), 1250031. https://doi.org/10.1142/S1793830912500310 doi: 10.1142/S1793830912500310
    [10] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem., 86 (2021), 11–16.
    [11] S. Mondal, N. De, A. Pal, Topological indices of some chemical structures applied for the treatment of covid-19 patients, Polycycl. Aromat. Comp., 42 (2022), 1220–1234. https://doi.org/10.1080/10406638.2020.1770306 doi: 10.1080/10406638.2020.1770306
    [12] S. Mondal, A. Dey, N. De, A. Pal, QSPR analysis of some novel neighbourhood degree-based topological descriptors, Complex Intell. Syst., 7 (2021), 977–996. https://doi.org/10.1007/s40747-020-00262-0 doi: 10.1007/s40747-020-00262-0
    [13] S. Mondal, K. C. Das, On the sanskruti index of graphs, J. Appl. Math. Comput., 69 (2023), 1205–1219. https://doi.org/10.1007/s12190-022-01789-w doi: 10.1007/s12190-022-01789-w
    [14] S. Mukwembi, On the upper bound of Gutman index of graphs, MATCH Commun. Math. Comput. Chem., 68 (2012), 343–348.
    [15] I. Redžepović, B. Furtula, Comparative study on structural sensitivity of eigenvalue-based molecular descriptors, J. Math. Chem., 59 (2021), 476–487. https://doi.org/10.1007/s10910-020-01202-6 doi: 10.1007/s10910-020-01202-6
    [16] J. A. Rodríguez-Velázquez, A. T Balaban, Two new topological indices based on graph adjacency matrix eigenvalues and eigenvectors, J. Math. Chem., 57 (2019), 1053–1074. https://doi.org/10.1007/s10910-019-01008-1 doi: 10.1007/s10910-019-01008-1
    [17] M. Shanmukha, N. Basavarajappa, K. Shilpa, A. Usha, Degree-based topological indices on anticancer drugs with QSPR analysis, Heliyon, 6 (2020). https://doi.org/10.1016/j.heliyon.2020.e04235 doi: 10.1016/j.heliyon.2020.e04235
    [18] J. Wei, M. F. Hanif, H. Mahmood, M. K. Siddiqui, M. Hussain, QSPR analysis of diverse drugs using linear regression for predicting physical properties, Polycycl. Aromat. Comp, 44 (2023), 4850–4870. https://doi.org/10.1080/10406638.2023.2257848 doi: 10.1080/10406638.2023.2257848
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(247) PDF downloads(83) Cited by(0)

Article outline

Figures and Tables

Figures(7)  /  Tables(3)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog