The $M$-matrix group inverse problem for distance-biregular graphs
Combinatorics
2022-04-29 v1
Abstract
In this paper we provide the group inverse of the combinatorial Laplacian matrix of distance-biregular graphs using the so-called equilibrium measures for sets obtained by deleting a vertex. We also show that the two equilibrium arrays characterizing a distance-biregular graph can be expressed in terms of the mentioned equilibrium measures. As a consequence of the minimum principle, we show a characterization of when the group inverse of the combinatorial Laplacian matrix of a distance-biregular graph is an -matrix.
Cite
@article{arxiv.2204.13186,
title = {The $M$-matrix group inverse problem for distance-biregular graphs},
author = {Aida Abiad and Ángeles Carmona and Andrés M. Encinas and María José Jiménez},
journal= {arXiv preprint arXiv:2204.13186},
year = {2022}
}