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arXiv · 2204.13186

The $M$-matrix group inverse problem for distance-biregular graphs

Aida Abiad·Ángeles Carmona·Andrés M. Encinas·María José Jiménez
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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 $M$-matrix.

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Aida Abiad, Ángeles Carmona, Andrés M. Encinas, María José Jiménez. 2022-04-27. The $M$-matrix group inverse problem for distance-biregular graphs. https://arxiv.org/abs/2204.13186

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