Distance-regular graphs where the distance-d graph has fewer distinct eigenvalues

2014/09/01 by A.E. Brouwer, A. E. Brouwer, M.A. Fiol +3
Mathematics · #05C50 #05E30 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Spectral Theory in Mathematical Physics #math.CO #msc:05C50 #msc:05E30

paper · pdf · doi:10.48550/arxiv.1409.0389

arxiv created 2014/09/01 · openalex publication_date 2014/09/01 · arxiv updated 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let the Kneser graph K of a distance-regular graph Γ be the graph on the same vertex set as Γ, where two vertices are adjacent when they have maximal distance in Γ. We study the situation where the Bose-Mesner algebra of Γ is not generated by the adjacency matrix of K. In particular, we obtain strong results in the so-called `half antipodal' case.

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