Abstract
In this work, we obtain the group inverse of the combinatorial Laplacian matrix of distance-biregular graphs. This expression can be obtained trough the so-called equilibrium measures for sets obtained by deleting a vertex. Moreover, we show that the two equilibrium arrays characterizing distance-biregular graphs can be expressed in terms of the mentioned equilibrium measures. As a consequence of the minimum principle, we provide a characterization of when the group inverse of the combinatorial Laplacian matrix of a distance-biregular graph is an M-matrix.
| Original language | English |
|---|---|
| Article number | 158 |
| Number of pages | 16 |
| Journal | Computational and Applied Mathematics |
| Volume | 42 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Jun 2023 |
Bibliographical note
Funding Information:The research of Á. Carmona, A.M. Encinas and M.J. Jiménez has been partly supported by the Spanish Research Council (Ministerio de Ciencia e Innovación) under project PID2021-122501NB-I00 and by the Universitat Politècnica de Catalunya under funds AGRUP-UPC. The research of A. Abiad is partially supported by the FWO grant 1285921N.
Funding
The research of Á. Carmona, A.M. Encinas and M.J. Jiménez has been partly supported by the Spanish Research Council (Ministerio de Ciencia e Innovación) under project PID2021-122501NB-I00 and by the Universitat Politècnica de Catalunya under funds AGRUP-UPC. The research of A. Abiad is partially supported by the FWO grant 1285921N.
Keywords
- Combinatorial Laplacian
- Distance-biregular graph
- Equilibrium measure
- Group inverse
- M-matrix