Resistance matrices of graphs with matrix weights

Authors

Fouzul Atik, SRM University-AP
R. B. Bapat, Indian Statistical Institute (Delhi Centre)
M. Rajesh Kannan, Indian Institute of Technology Kharagpur

Article Type

Research Article

Publication Title

Linear Algebra and Its Applications

Abstract

The resistance matrix of a simple connected graph G is denoted by R, and is defined by R=(r ij ), where r ij is the resistance distance between the vertices i and j of G. In this paper, we consider the resistance matrix of weighted graph with edge weights being positive definite matrices of same size. We derive a formula for the determinant and the inverse of the resistance matrix. Then, we establish an interlacing inequality for the eigenvalues of resistance and Laplacian matrices of tree. Using this interlacing inequality, we obtain the inertia of the resistance matrix of tree.

First Page

41

Last Page

57

DOI

10.1016/j.laa.2019.02.011

Publication Date

6-15-2019

Comments

Open Access, Green

Recommended Citation

Atik, Fouzul; Bapat, R. B.; and Rajesh Kannan, M., "Resistance matrices of graphs with matrix weights" (2019). Journal Articles. 800.
https://digitalcommons.isical.ac.in/journal-articles/800