Title

Resistance matrices of balanced directed graphs

Article Type

Research Article

Publication Title

Linear and Multilinear Algebra

Abstract

Let G be a strongly connected and balanced directed graph. We define the resistance rij between any two vertices i and j of G by using the Moore–Penrose inverse of the Laplacian matrix of G and define the resistance matrix by R := [rij]. This generalizes the resistance in the undirected case. In this paper, we show that R is a non-negative matrix and obtain an expression to compute the inverse, determinant and cofactor sums of R.

DOI

10.1080/03081087.2020.1748850

Publication Date

1-1-2020

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