Abstract
AbstractIn 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.
Funder
FWO
Ministerio de Ciencia e Innovacion
Universitat Politecnica de Catalunya
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics