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

Yaxin Jiang and Yujun Yang

Applied Mathematics and Computation, 2025, vol. 496, issue C

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].

Keywords: Resistance distance; Kirchhoff index; Mesh-star transformation (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:496:y:2025:i:c:s0096300325000815

DOI: 10.1016/j.amc.2025.129354

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