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The (Multiplicative Degree‐) Kirchhoff Index of Graphs Derived from the Cartesian Product of Sn and K2

Author

Listed:
  • Jia-Bao Liu
  • Xin-Bei Peng
  • Jiao-Jiao Gu
  • Wenshui Lin

Abstract

It is well known that many topological indices have widespread use in lots of fields about scientific research, and the Kirchhoff index plays a major role in many different sectors over the years. Recently, Li et al. (Appl. Math. Comput. 382 (2020) 125335) proposed the problem of determining the Kirchhoff index and multiplicative degree‐Kirchhoff index of graphs derived from Sn × K2, the Cartesian product of the star Sn, and the complete graph K2. In the present study, we completely solve this problem, that is, the explicit closed‐form formulae of the Kirchhoff index, multiplicative degree‐Kirchhoff index, and number of spanning trees are obtained for some graphs derived from Sn × K2.

Suggested Citation

  • Jia-Bao Liu & Xin-Bei Peng & Jiao-Jiao Gu & Wenshui Lin, 2022. "The (Multiplicative Degree‐) Kirchhoff Index of Graphs Derived from the Cartesian Product of Sn and K2," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:1670984
    DOI: 10.1155/2022/1670984
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    References listed on IDEAS

    as
    1. S. Kavithaa & V. Kaladevi, 2017. "Gutman Index and Detour Gutman Index of Pseudo-Regular Graphs," Journal of Applied Mathematics, Hindawi, vol. 2017, pages 1-8, August.
    2. 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.
    3. 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).
    4. S. Kavithaa & V. Kaladevi, 2017. "Gutman Index and Detour Gutman Index of Pseudo‐Regular Graphs," Journal of Applied Mathematics, John Wiley & Sons, vol. 2017(1).
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