Characterizing \((\ell ,m)\)-walk-regular graphs

DOI10.1016/j.laa.2010.06.042zbMath1213.05164OpenAlexW2003893924MaRDI QIDQ603112

C. Dalfó, E. Garriga, Miquel Àngel Fiol

Publication date: 5 November 2010

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2010.06.042

zbMATH Keywords

distance-regular graphspectrumadjacency matrixpredistance polynomialwalk-regular graphpreintersection number

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Distance in graphs (05C12)

Related Items (11)

2-walk-regular dihedrants from group-divisible designs ⋮ A spectral equivalent condition of the \(P\)-polynomial property for association schemes ⋮ A simple approach for lower-bounding the distortion in any hyperbolic embedding ⋮ On almost distance-regular graphs ⋮ Geometric aspects of 2-walk-regular graphs ⋮ A characterization of bipartite distance-regular graphs ⋮ 2-walk-regular graphs with a small number of vertices compared to the valency ⋮ Equivalent characterizations of the spectra of graphs and applications to measures of distance-regularity ⋮ On 2-walk-regular graphs with a large intersection number \(c_2\) ⋮ The 2-partially distance-regular graphs such that their second largest local eigenvalues are at most one ⋮ Thin \(Q\)-polynomial distance-regular graphs have bounded \(c_2\)

Cites Work

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• On \(k\)-walk-regular graphs
• Feasibility conditions for the existence of walk-regular graphs
• The alternating and adjacency polynomials, and their relation with the spectra and diameters of graphs
• Problems in algebraic combinatorics
• From local adjacency polynomials to locally pseudo-distance-regular graphs
• On the Polynomial of a Graph

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