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Resistance distance-based graph invariants and spanning trees of graphs derived from the strong prism of a star

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  • Li, Zhemin
  • Xie, Zheng
  • Li, Jianping
  • Pan, Yingui

Abstract

Let Sn2 be the graph obtained by the strong prism of a star Sn, i.e. the strong product of K2 and Sn. In this paper, explicit expressions for Kirchhoff index, multiplicative degree-Kirchhoff index and number of spanning tress of Sn2 are determined, respectively. More specially, let Sn,r2 be the set of subgraphs obtained by randomly deleting r vertical edges from Sn2, where 0 ≤ r ≤ n. Explicit formulas for Kirchhoff index and number of spanning trees for any graph Sn,r2∈Sn,r2 are established, respectively. Moreover, the Kirchhoff index of Sn,r2 is almost three-eighths of its Wiener index.

Suggested Citation

  • Li, Zhemin & Xie, Zheng & Li, Jianping & Pan, Yingui, 2020. "Resistance distance-based graph invariants and spanning trees of graphs derived from the strong prism of a star," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    • Handle: RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320303015
    DOI: 10.1016/j.amc.2020.125335
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    References listed on IDEAS

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    1. Huang, Jing & Li, Shuchao & Li, Xuechao, 2016. "The normalized Laplacian, degree-Kirchhoff index and spanning trees of the linear polyomino chains," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 324-334.
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    Cited by:

    1. Sun, Wensheng & Yang, Yujun, 2023. "Extremal pentagonal chains with respect to the Kirchhoff index," Applied Mathematics and Computation, Elsevier, vol. 437(C).

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