Research article

Multiplicative topological properties of graphs derived from honeycomb structure

  • Received: 29 October 2019 Accepted: 16 January 2020 Published: 04 February 2020
  • MSC : 05C12, 05C90

  • Topological indices are numerical parameters of a molecular graph, which characterize its topology and are usually graph invariant. In quantitative structure-activity relationship/quantitative structure-property relationship study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC), and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we are taking Dominating David Derived networks, produced by honeycomb structure of dimension t and obtain analytical closed results of Multiplicative topological indices and acquire exact results of degree based indices.

    Citation: Usman Babar, Haidar Ali, Shahid Hussain Arshad, Umber Sheikh. Multiplicative topological properties of graphs derived from honeycomb structure[J]. AIMS Mathematics, 2020, 5(2): 1562-1587. doi: 10.3934/math.2020107

    Related Papers:

  • Topological indices are numerical parameters of a molecular graph, which characterize its topology and are usually graph invariant. In quantitative structure-activity relationship/quantitative structure-property relationship study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC), and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we are taking Dominating David Derived networks, produced by honeycomb structure of dimension t and obtain analytical closed results of Multiplicative topological indices and acquire exact results of degree based indices.


    加载中


    [1] H. Ali, A. Sajjad, On further results of hex derived networks, Open J. Discret. Appl. Math., 2 (2019), 32-40. doi: 10.30538/psrp-odam2019.0009
    [2] H. Ali, M. A. Binyamin, M. K. Shafiq, et al. On the Degree-Based Topological Indices of Some Derived Networks, Mathematics, 7 (2019), 612.
    [3] M. Bača, J. Horváthová, M. Mokrišová, et al. On topological indices of carbon nanotube network, Can. J. Chem. 93 (2015), 1-4.
    [4] A. Q. Baig, M. Imran, H. Ali, On Topological Indices of Poly Oxide, Poly Silicate, DOX and DSL Networks, Can. J. Chem., 93 (2015), 730-739.
    [5] A. Q. Baig, M. Imran, H. Ali, et al. Computing topological polynomials of certain nanostructures, J. Optoelectron. Adv. M., 17 (2015), 877-883.
    [6] M. V. Diudea, I. Gutman, J. Lorentz, Molecular Topology, Nova Science Publishers: Huntington, NY, USA, 2001.
    [7] M. Deza, P. W. Fowler, A. Rassat, et al. Fullerenes as tiling of surfaces, J. Chem. Inf. Comput. Sci., 40 (2000), 550-558. doi: 10.1021/ci990066h
    [8] M. Eliasi, A. Iranmanesh, I. Gutman, Multiplicative versions of first Zagreb index, Match-Communications in Mathematical and Computer Chemistry, 68 (2012), 217.
    [9] W. Gao, M. K. Siddiqui, M. Naeem, et al. Computing multiple ABC index and multiple GA index of some grid graphs, Open Physics, 16 (2018), 588-598. doi: 10.1515/phys-2018-0077
    [10] I. Gutman, S. J. Cyvin, Introduction to the Theory of Benzenoid Hydrocarbons, Springer: Berlin, Germany, 1989.
    [11] I. Gutman, B. Rusić, N. Trinajstić, et al. Graph theory and molecular orbitals. XⅡ. Acyclic polyenes, The Journal of Chemical Physics, 62 (1975), 3399-3405. doi: 10.1063/1.430994
    [12] M. Imran, A. Q. Baig, H. Ali, On topological properties of dominating David derived networks, Can. J. Chem., 94 (2015), 137-148.
    [13] M. Imran, A. Q. Baig, S. U. Rehman, et al. Computing topological polynomials of mesh-derived networks, Discret. Math. Algorithms Appl., 10 (2018), 1850077.
    [14] M. Imran, A. Q. Baig, H. M. A. Siddiqui, et al. On molecular topological properties of diamond like networks, Can. J. Chem., 95 (2017), 758-770. doi: 10.1139/cjc-2017-0206
    [15] V. R. Kulli, Multiplicative hyper-Zagreb indices and coindices of graphs: Computing these indices of some nanostructures, International Research Journal of Pure Algebra, 6 (2016), 342-347.
    [16] J. B. Liu, A. Q. Baig, W. Khalid, et al. Multiplicative indices of carbon graphite t-levels, Comptes rendus de l'Académie bulgare des Sciences, 17(2018), 10-21.
    [17] J. B. Liu, J. Zhao, Z. Q. Cai, On the generalized adjacency, Laplacian and signless Laplacian spectra of the weighted edge corona networks, Physica A: Statistical Mechanics and Its Applications, 540 (2020), 123073.
    [18] J. B. Liu, J. Zhao, H. He, et al. Valency-based topological descriptors and structural property of the generalized sierpiński networks, Journal of Statistical Physics, 177 (2019), 1131-1147. doi: 10.1007/s10955-019-02412-2
    [19] J. B. Liu, J. Zhao, J. Min, et al. The hosoya index of graphs formed by a fractal graph, Fractals, (2019), 1950135.
    [20] J. B. Liu, J. Zhao, Z. Zhu, On the number of spanning trees and normalized Laplacian of linear octagonal-quadrilateral networks, International Journal of Quantum Chemistry, 119 (2019), e25971.
    [21] A. Nayak, I. Stojmenovic, Hand Book of Applied Algorithms: Solving Scientific, Engineering, and Practical Problems, John Wiley and Sons: Hoboken, NJ, USA, 2007; 560p.
    [22] F. Simonraj, A. George, Embedding of poly honeycomb networks and the metric dimension of star of david network, GRAPH-HOC, 4 (2012), 11-28. doi: 10.5121/jgraphoc.2012.4402
    [23] F. Simonraj, A. George, On the Metric Dimension of HDN3 and PHDN3, Proceedings of the IEEE International Conference on Power, Control, Signals and Instrumentation Engineering (ICPCSI), (2017), 1333-1336.
    [24] I. Stojmenovic, Honeycomb networks: Topological properties and communication algorithms, IEEE Transactions on parallel and distributed systems, 8 (1997), 1036-1042. doi: 10.1109/71.629486
    [25] Star of David [online]. Available from: http://en.wikipedia.org/wiki/StarofDavid.
    [26] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc., 69 (1947), 17-20. doi: 10.1021/ja01193a005
    [27] C. C. Wei, H. Ali, M. A. Binyamin, et al. Computing Degree Based Topological Properties of Third Type of Hex-Derived Networks, Mathematics, 7 (2019), 368.
  • 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(2008) PDF downloads(388) Cited by(1)

Article outline

Figures and Tables

Figures(7)  /  Tables(6)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog