The M-matrix group inverse problem for distance-biregular graphs
| Autor: | Aida Abiad, Ángeles Carmona, Andrés M. Encinas, María José Jiménez |
|---|---|
| Přispěvatelé: | Mathematics, Digital Mathematics, EAISI Foundational, Combinatorial Optimization 1, Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. OMGRAPH - Optimisation Methods on Graphs |
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
Equilibrium measure
Distance-biregular graph Applied Mathematics 15 Linear and multilinear algebra matrix theory [Classificació AMS] Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC] Applied mathematics Matemàtica aplicada Computational Mathematics Combinatorial Laplacian Mathematics::Algebraic Geometry Group inverse 51 Geometry::51E Finite geometry and special incidence structures [Classificació AMS] FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) M-matrix 05 Combinatorics::05C Graph theory [Classificació AMS] |
| Zdroj: | Computational and Applied Mathematics, 42(4):158. Springer |
| ISSN: | 2238-3603 |
| DOI: | 10.1007/s40314-023-02301-1 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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