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Analyzing lattice networks through substructures

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  • Lei, Hui
  • Li, Tao
  • Ma, Yuede
  • Wang, Hua

Abstract

Analyzing the topology of network structures is an important topic studied from many different aspects of science and mathematics. The Wiener polarity index (number of unordered pairs of vertices at distance 3 from each other) is one of the representative descriptors of graph structures. It was computed for several lattice networks by Chen et al. [11] in an effort to understand the properties of these networks. The Wiener polarity index is a variation of the classic distance-based graph invariant, the Wiener index (sum of distances between all pairs of vertices), which is known to be closely related to the number of substructures. In this paper we examine the numbers of various subgraphs of order 4 for these lattice networks. In addition to confirming their symmetric nature, comparing the numbers of various substructures leads to insights on other less trivial characteristics of these network structures of common interest.

Suggested Citation

  • Lei, Hui & Li, Tao & Ma, Yuede & Wang, Hua, 2018. "Analyzing lattice networks through substructures," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 297-314.
    • Handle: RePEc:eee:apmaco:v:329:y:2018:i:c:p:297-314
    DOI: 10.1016/j.amc.2018.02.012
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    References listed on IDEAS

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    1. Cao, Shujuan & Dehmer, Matthias & Kang, Zhe, 2017. "Network Entropies Based on Independent Sets and Matchings," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 265-270.
    2. Zhang, Yanhong & Hu, Yumei, 2016. "The Nordhaus–Gaddum-type inequality for the Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 880-884.
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    4. Yu, Guihai & Liu, Xin & Qu, Hui, 2017. "Singularity of Hermitian (quasi-)Laplacian matrix of mixed graphs," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 287-292.
    5. Hua, Hongbo & Das, Kinkar Ch., 2016. "On the Wiener polarity index of graphs," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 162-167.
    6. Liu, Jia-Bao & Pan, Xiang-Feng, 2015. "Asymptotic incidence energy of lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 193-202.
    7. Liu, Jia-Bao & Pan, Xiang-Feng, 2015. "A unified approach to the asymptotic topological indices of various lattices," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 62-73.
    8. Liu, Jia-Bao & Pan, Xiang-Feng & Hu, Fu-Tao & Hu, Feng-Feng, 2015. "Asymptotic Laplacian-energy-like invariant of lattices," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 205-214.
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    Cited by:

    1. Ali, Akbar & Du, Zhibin & Ali, Muhammad, 2018. "A note on chemical trees with minimum Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 231-236.
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    9. Noureen, Sadia & Bhatti, Akhlaq Ahmad & Ali, Akbar, 2021. "Towards the solution of an extremal problem concerning the Wiener polarity index of alkanes," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
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