Dual concepts of almost distance-regularity and the spectral excess theorem

DOI10.1016/j.disc.2012.03.003zbMath1245.05032arXiv1207.3606OpenAlexW2155463583MaRDI QIDQ442405

C. Dalfó, E. Garriga, Miquel Àngel Fiol, van Dam, Edwin R.

Publication date: 10 August 2012

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.3606

zbMATH Keywords

idempotentsdistance-regular grapheigenvalueslocal spectrumpredistance polynomialsdistance matrices

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Distance in graphs (05C12)

Related Items

A spectral equivalent condition of the \(P\)-polynomial property for association schemes ⋮ A spectral excess theorem for nonregular graphs ⋮ A characterization of bipartite distance-regular graphs ⋮ A spectral excess theorem for normal digraphs ⋮ A spectral excess theorem for digraphs with normal Laplacian matrices ⋮ Algebraic characterizations of regularity properties in bipartite graphs

Cites Work

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• A simple proof of the spectral excess theorem for distance-regular graphs
• The spectral excess theorem for distance-regular graphs: a global (over)view
• On \(k\)-walk-regular graphs
• Locally pseudo-distance-regular graphs
• Problems in algebraic combinatorics
• Algebraic characterizations of distance-regular graphs
• From local adjacency polynomials to locally pseudo-distance-regular graphs
• Some families of orthogonal polynomials of a discrete variable and their applications to graphs and codes
• On almost distance-regular graphs
• On the Polynomial of a Graph
• On pseudo-distance-regularity

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