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

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-bi...

Descripción completa

Detalles Bibliográficos
Autores: Abiad Monge, Aida, Carmona Mejías, Ángeles|||0000-0001-7713-1066, Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373, Jiménez Jiménez, María José|||0000-0003-3502-462X
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/387555
Acceso en línea:https://hdl.handle.net/2117/387555
https://dx.doi.org/10.1007/s40314-023-02301-1
Access Level:acceso abierto
Palabra clave:Applied mathematics
Matemàtica aplicada
Classificació AMS::51 Geometry::51E Finite geometry and special incidence structures
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
Descripción
Sumario: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.