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

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 18 Apr 2023Embargo end date: 01 Jan 2022 English Publisher:Springer Science and Business Media LLCJournal:Computational and Applied Mathematics, volume 42 (issn: 2238-3603, eissn: 1807-0302,

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Authors: Abiad Monge, Aida; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, María José;

doi: 10.1007/s40314-023-02301-1 , 10.48550/arxiv.2204.13186

arXiv: 2204.13186

handle: 2117/387555 , 20.500.14017/d85bb3f8-a101-440c-9efc-b691e77ad8dc

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

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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.

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Vrije Universiteit Brussel
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Eindhoven University of Technology
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Keywords

Equilibrium measure, \(M\)-matrix, Distance-biregular graph, Classificació AMS::05 Combinatorics::05C Graph theory, Matemàtica aplicada, group inverse, Group inverse, matrix theory, FOS: Mathematics, Mathematics - Combinatorics, Theory of matrix inversion and generalized inverses, Classificació AMS::51 Geometry::51E Finite geometry and special incidence structures, Classificació AMS::15 Linear and multilinear algebra; matrix theory, Graphs and linear algebra (matrices, eigenvalues, etc.), combinatorial Laplacian, Applied mathematics, General block designs in finite geometry, Classificació AMS::15 Linear and multilinear algebra, Combinatorial Laplacian, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, distance-biregular graph, Combinatorics (math.CO), M-matrix, Generalized quadrangles and generalized polygons in finite geometry, equilibrium measure

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