2026-04-13T04:53:58Zhttps://recercat.cat/oai/requestoai:recercat.cat:10459.1/4632532025-09-15T18:05:33Zcom_2072_3622col_2072_479130
RECERCAT
author
Dalfó, Cristina
author
Fiol Mora, Miguel Ángel
author
Garriga, Ernest
2010-12-30
A graph G with diameter D and d + 1 distinct eigenvalues is said to be (ℓ, m)-walk-regular, for some integers ℓ ∈ [0, d] and m ∈
[0, D], ℓ≥ m, if the number of walks of length i ∈ [0, ℓ] between any pair of vertices at distance j ∈ [0, m] depends only on the values of
i and j. In this paper, we study some algebraic and combinatorial characterizations of (ℓ, m)-walk-regularity based on the so-called
predistance polynomials and the preintersection numbers.Research supported by the Ministerio de Educación y Ciencia (Spain) and the European Regional Development Fund under project MTM2008-06620-C03-01, and by the Catalan Research Council under project 2009SGR1387.
cc-by-nc-nd, (c) Elsevier, 2010 Attribution-NonCommercial-NoDerivatives 4.0 International info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/
Distance-regular graph
Walk-regular graph
Adjacency matrix
Spectrum
Predistance polynomial
Preintersection number
Characterizing (ℓ,m)-walk-regular graphs
info:eu-repo/semantics/acceptedVersion