Distance-regular graphs with exactly one positive q-distance eigenvalue

2023/05/24 by Jack H. Koolen, Koolen, Jack H., Mamoon Abdullah +5
Computer Science · Engineering · Mathematics · #05C50 #05E30 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2305.14636

openalex publication_date 2023/05/24 · openalex created_date 2023/05/27 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the q-distance matrix for a distance-regular graph and show that the q-distance matrix of a distance-regular graph with classical parameters (D, q, α, β) has exactly three distinct eigenvalues, of which one is zero. Moreover, we study distance-regular graphs whose q-distance matrix has exactly one positive eigenvalue.

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