Research article Special Issues

On leap Zagreb indices of bridge and chain graphs

  • Received: 26 June 2020 Accepted: 13 August 2020 Published: 20 August 2020
  • MSC : 05C07, 05C35, 05C40

  • The 2-degree of a vertex v in a (molecular) graph G is the number of vertices which are at distance two from v in G. The first leap Zagreb index of a graph G is the sum of squares of the 2-degree of all vertices in G and the third leap Zagreb index of G is the sum of product of the degree and 2-degree of every vertex v in G. In this paper, we compute the first and third leap Zagreb indices of bridge and chain graphs. Also we apply these results to determine the first and third leap Zagreb indices of some chemical structures such as polyphenyl chains and spiro chains.

    Citation: Natarajan Chidambaram, Swathi Mohandoss, Xinjie Yu, Xiujun Zhang. On leap Zagreb indices of bridge and chain graphs[J]. AIMS Mathematics, 2020, 5(6): 6521-6536. doi: 10.3934/math.2020420

    Related Papers:

  • The 2-degree of a vertex v in a (molecular) graph G is the number of vertices which are at distance two from v in G. The first leap Zagreb index of a graph G is the sum of squares of the 2-degree of all vertices in G and the third leap Zagreb index of G is the sum of product of the degree and 2-degree of every vertex v in G. In this paper, we compute the first and third leap Zagreb indices of bridge and chain graphs. Also we apply these results to determine the first and third leap Zagreb indices of some chemical structures such as polyphenyl chains and spiro chains.


    加载中


    [1] M. Azari, A. Iranmanesh, I. Gutman, Zagreb indices of bridge and chain graphs, Math. Commun. Math. Comput. Chem., 70 (2013), 921-938.
    [2] B. Basavanagoud, E. Chitra, On leap Hyper-Zagreb indices of some nanostructures, Int. J. Math. Trends Tech., 64 (2018), 30-36. doi: 10.14445/22315373/IJMTT-V64P505
    [3] I. Gutman, K. C. Das, The first Zagreb index 30 years after, Math. Commun. Math. Comput. Chem., 50 (2004), 83-92.
    [4] I. Gutman, N. Trinajstić, Graph theory and molecular orbitals-total electron energy of alternate hydrocarbons, J. Chem. Phys. Lett., 9 (1972), 535-538.
    [5] I. Gutman, M. Emina, M. Igor, Beyond the Zagreb indices, AKCE Int. J. Comb., Available from: https://www.sciencedirect.com/science/article/pii/S0972860017302359, https://doi.org/10.1016/j.akcej.2018.05.002.
    [6] J. A. Jerline, K. Dhanalakshmi, L. B. M. Raj, Harmonic index of bridge and chain graphs, Int. J. Math. Appl., 5 (2017), 275-284.
    [7] V. R. Kulli, Leap indices of graphs, Int. J. Cur. Res. Life Sci., 8 (2019), 2998-3006.
    [8] V. R. Kulli, Product connectivity leap index and ABC leap index of Helm graphs, Ann. Pure Appl. Math., 18 (2018), 189-192. doi: 10.22457/apam.v18n2a8
    [9] V. R. Kulli, on F-leap indices and F-leap polynomials of some graphs, Int. J. Math. Archive, 9 (2018), 41-49.
    [10] E. Litta, J. J. Amalorpava, K. Dhanalakshmi, et al. Modified Zagreb indices of bridge graphs, Int. J. Math. Archive, 8 (2017), 86-91.
    [11] M. A. Mohammed, R. S. Haoer, J. Robert, et al. F-leap index of some special classes of bridge and chain graphs, Eurasian Chem. Commun., 2 (2020), 827-833. doi: 10.33945/SAMI/ECC.2020.7.10
    [12] X. J. Zhang, X. L. Wu, S. Akhter, et al. Edge-version Atom-Bond connectivity and geometric arithmetic indices of generalized bridge molecular graphs, Symmetry, 10 (2018), 1-16.
    [13] A. M. Naji, N. D. Soner, I. Gutman, On leap Zagreb indices of graphs, Commun. Comb. Opt., 2 (2017), 99-117.
    [14] A. M. Naji, B. Davvaz, S. S. Mahde, et al. A study on some properties of leap graphs, Commun. Comb. Opt., 5 (2020), 9-17.
    [15] N. De, Hyper Zagreb index of bridge and chain graphs, Open J. Math. Sci., 2 (2018), 1-17.
    [16] N. De, F-index of bridge and chain graphs, Mal. J. Fund. Appl. Sci., 12 (2016), 109-113.
    [17] P. Shiladhar, A. M. Naji, N. D. Soner, Computation of leap Zagreb indices of some windmill graphs, Int. J. Math. Appl., 6 (2018), 183-191.
    [18] Z. H. Shao, I. Gutman, Z. P. Li, et al. Leap Zagreb indices of trees and unicyclic graphs, Commun. Comb. Opt., 3 (2018), 179-184.
  • Reader Comments
  • © 2020 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(3010) PDF downloads(212) Cited by(2)

Article outline

Figures and Tables

Figures(9)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog