The \(M\)-matrix group inverse problem for distance-biregular graphs

DOI10.1007/s40314-023-02301-1zbMath1524.15006arXiv2204.13186MaRDI QIDQ6044750

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Publication date: 22 May 2023

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.13186

zbMATH Keywords

\(M\)-matrixgroup inverseequilibrium measurecombinatorial Laplaciandistance-biregular graph

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Generalized quadrangles and generalized polygons in finite geometry (51E12) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) General block designs in finite geometry (51E05)

Cites Work

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• The spectral excess theorem for distance-biregular graphs.
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• Derivatives of the Perron root at an essentially nonnegative matrix and the group inverse of an M-matrix
• Generalized inverses of symmetric \(M\)-matrices
• Distance-biregular graphs with 2-valent vertices and distance regular line graphs
• Designs with no three mutually disjoint blocks
• Bipartite distance-regular graphs. I
• Distance biregular bipartite graphs
• Heat kernel and Green kernel comparison theorems for infinite graphs
• Discrete Green's functions
• Moore-Penrose inverse of incidence matrix of graphs with complete and cyclic blocks
• Distance-regularised graphs are distance-regular or distance-biregular
• More on generalizations of matrix monotonicity
• Solving Dirichlet and Poisson problems on graphs by means of equilibrium measures
• Group inverses of \(M\)-matrices associated with nonnegative matrices having few eigenvalues
• Bipartite distance-regular graphs. II
• Shortest paths in distance-regular graphs
• Solving boundary value problems on networks using equilibrium measures
• Moore-Penrose inverse of the incidence matrix of a distance regular graph
• On the distance spectrum of minimal cages and associated distance biregular graphs
• Matrices whose group inverses are \(M\)-matrices
• The Moore-Penrose inverse of the incidence matrix of complete multipartite and bi-block graphs
• Discrete elliptic operators and their Green operators
• A note on distance-regular graphs with a small number of vertices compared to the valency
• Distance–regular graphs having theM-property
• The M-Matrix Group Generalized Inverse Problem for Weighted Trees
• Group generalized inverses of M-matrices associated with periodic and nonperiodic jacobi matrices

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