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On the Asymptotic Network Indices of Weighted Three-Layered Structures with Multi-Fan Composed Subgraphs

Author

Listed:
  • Jicheng Bian

    (School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China)

  • Da Huang

    (School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China)

  • Jian Zhu

    (School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China
    School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China)

  • Xing Chen

    (School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China)

Abstract

In this paper, three sorts of network indices for the weighted three-layered graph are studied through the methods of graph spectra theory combined with analysis methods. The concept of union of graphs are applied to design two sorts of weighted layered multi-fan composed graphs, and the accurate mathematical expressions of the network indices are obtained through the derivations of Laplacian spectra; furthermore, the asymptotic properties are also derived. We find that when the cardinalities of the vertices on a sector-edge-link tend to infinity, the indices of FONC and EMFPT are irrelevant with the number of copies of the fan-substructure based on the considered graph framework.

Suggested Citation

  • Jicheng Bian & Da Huang & Jian Zhu & Xing Chen, 2024. "On the Asymptotic Network Indices of Weighted Three-Layered Structures with Multi-Fan Composed Subgraphs," Mathematics, MDPI, vol. 12(15), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2359-:d:1444770
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    References listed on IDEAS

    as
    1. Xiaoqian Wang & Meifeng Dai & Yufei Chen & Yue Zong & Yu Sun & Weiyi Su, 2018. "Determining entire mean first-passage time for Cayley networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 29(01), pages 1-10, January.
    2. Jia-Bao Liu & Yan Bao & Wu-Ting Zheng & Sakander Hayat, 2021. "NETWORK COHERENCE ANALYSIS ON A FAMILY OF NESTED WEIGHTED n-POLYGON NETWORKS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-15, December.
    3. 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.
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