Resistance distances in vertex-weighted complete multipartite graphs

Wuxian Chen and Weigen Yan

Applied Mathematics and Computation, 2021, vol. 409, issue C

Abstract: Let G be a vertex-weighted complete multipartite graph with vertex set V and edge set E, and vertex-weighted function ω:V→R+. This results in an edge-weighted network graph in which the weight (resistance) of every edge (u,v)∈E equals ω(u)ω(v). Gervacio (Discrete Appl. Math. 203 (2016) 53–61) derived the formula to compute the resistance distances between two vertices of the complete multipartite graph where each vertex has a weight of 1. In this paper, we generalize the Gervacio’s result and obtain the formula to compute the resistance distance between any two vertices in the vertex-weighted complete multipartite network graph.

Keywords: Resistance; Vertex-weighted network graph; Complete multipartite graph; Star-triangle transformation (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321004719

DOI: 10.1016/j.amc.2021.126382

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