Resistance matrices of balanced directed graphs

Authors

R. Balaji, Indian Institute of Technology Madras
R. B. Bapat, Indian Statistical Institute (Delhi Centre)
Shivani Goel, Indian Institute of Technology Madras

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 (Formula presented.) 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 (Formula presented.). 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.

First Page

787

Last Page

808

DOI

10.1080/03081087.2020.1748850

Publication Date

1-1-2022

Comments

Open Access, Green

Recommended Citation

Balaji, R.; Bapat, R. B.; and Goel, Shivani, "Resistance matrices of balanced directed graphs" (2022). Journal Articles. 3437.
https://digitalcommons.isical.ac.in/journal-articles/3437