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Computation of resistance distances and Kirchhoff indices for two classes of graphs

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  • Jiang, Yaxin
  • Yang, Yujun

Abstract

For any two vertices u and v of a connected graph G, the resistance distance between u and v is defined as the effective resistance between them in the corresponding electrical network created by placing a unit resistor on each edge of G. The Kirchhoff index of G is defined as the sum of resistance distances between all pairs of vertices in G. Let Kr− be the graph obtained from the complete graph Kr by deleting an edge. In this paper, we consider two classes of graphs formed by Kr−, namely the string graph of Kr− and the ring graph of Kr−, which are denoted by S(Kr−,n) and R(Kr−,n), respectively. By using combinatorial and electrical network approaches, we obtain the formulae for resistance distances and Kirchhoff indices of S(Kr−,n) and R(Kr−,n), which generalizes the results by Sardar et al. (2024) [25].

Suggested Citation

  • Jiang, Yaxin & Yang, Yujun, 2025. "Computation of resistance distances and Kirchhoff indices for two classes of graphs," Applied Mathematics and Computation, Elsevier, vol. 496(C).
    • Handle: RePEc:eee:apmaco:v:496:y:2025:i:c:s0096300325000815
    DOI: 10.1016/j.amc.2025.129354
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    References listed on IDEAS

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    1. Sardar, Muhammad Shoaib & Pan, Xiang-Feng & Xu, Shou-Jun, 2024. "Computation of the resistance distance and the Kirchhoff index for the two types of claw-free cubic graphs," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    2. Jiang, Zhuozhuo & Yan, Weigen, 2017. "Resistance between two nodes of a ring network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 21-26.
    3. Sardar, Muhammad Shoaib & Pan, Xiang-Feng & Xu, Si-Ao, 2020. "Computation of resistance distance and Kirchhoff index of the two classes of silicate networks," Applied Mathematics and Computation, Elsevier, vol. 381(C).
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