Algebraic characterizations of distance-regular graphs
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Publication:1348144
DOI10.1016/S0012-365X(01)00255-2zbMath1025.05060OpenAlexW2057731281WikidataQ126819181 ScholiaQ126819181MaRDI QIDQ1348144
Publication date: 15 May 2002
Published in: Discrete Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0012-365x(01)00255-2
Association schemes, strongly regular graphs (05E30) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Structural characterization of families of graphs (05C75)
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Corrigendum to ``Algebraic characterizations of regularity properties in bipartite graphs ⋮ Multipartite Moore digraphs ⋮ Minimum cuts of distance-regular digraphs ⋮ Edge-distance-regular graphs are distance-regular ⋮ The spectral excess theorem for distance-biregular graphs. ⋮ A characterization and an application of weight-regular partitions of graphs ⋮ On almost distance-regular graphs ⋮ A spectral excess theorem for nonregular graphs ⋮ Dual concepts of almost distance-regularity and the spectral excess theorem ⋮ On symmetric association schemes and associated quotient-polynomial graphs ⋮ A characterization of bipartite distance-regular graphs ⋮ Pseudo-distance-regularized graphs are distance-regular or distance-biregular ⋮ The spectral excess theorem for distance-regular graphs having distance-\(d\) graph with fewer distinct eigenvalues ⋮ An odd characterization of the generalized odd graphs ⋮ Weakly distance-regular digraphs. ⋮ A spectral excess theorem for normal digraphs ⋮ Spectral bounds for the \(k\)-independence number of a graph ⋮ The local spectra of regular line graphs ⋮ A simple proof of the spectral excess theorem for distance-regular graphs ⋮ Some spectral and quasi-spectral characterizations of distance-regular graphs ⋮ Algebraic characterizations of graph regularity conditions ⋮ Edge-distance-regular graphs ⋮ On perturbations of almost distance-regular graphs ⋮ Spectral bounds and distance-regularity ⋮ The geometry oft-spreads ink-walk-regular graphs ⋮ A spectral excess theorem for digraphs with normal Laplacian matrices ⋮ On the spectrum of an extremal graph with four eigenvalues ⋮ Algebraic characterizations of regularity properties in bipartite graphs ⋮ Equivalent characterizations of the spectra of graphs and applications to measures of distance-regularity ⋮ On a version of the spectral excess theorem ⋮ On the weak distance-regularity of Moore-type digraphs ⋮ Optimization of eigenvalue bounds for the independence and chromatic number of graph powers ⋮ On the hierarchical product of graphs and the generalized binomial tree ⋮ The spectral excess theorem for graphs with few eigenvalues whose distance-2 or distance-1-or-2 graph is strongly regular ⋮ On Middle Cube Graphs ⋮ Graphs, friends and acquaintances ⋮ A general method to obtain the spectrum and local spectra of a graph from its regular partitions
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