Resistance distances in vertex-weighted complete multipartite graphs.

• We weight the complete multipartite graphs. • We compute the resistance distances of the vertex-weighted complete multipartite graphs. • We generalize the Gervacio's result on the resistance distances of the complete multipartite graphs. 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. [ABSTRACT FROM AUTHOR]