The Pseudo Cosine Sequences of a Distance-Regular Graph

2003/12/08 by Arlene A. Pascasio, Paul Terwilliger, Pascasio, Arlene A. +1
Computer Science · Mathematics · #05E50 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Rings, Modules, and Algebras #math.CO #msc:05E50

paper · pdf · doi:10.48550/arxiv.math/0312150

25 pages

arxiv created 2003/12/08 · openalex publication_date 2003/12/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G denote a distance-regular graph with diameter D≥ 3, valency k, and intersection numbers a_i, b_i, c_i. By a \it pseudo cosine sequence of G we mean a sequence of real numbers s₀, s₁, ..., s_D such that s₀=1 and c_i s_i-1+a_i s_i+b_i s_i+1=k s₁ s_i for 0 ≤ i ≤ D-1. Let s₀, s₁,..., s_D and p₀, p₁, ..., p_D denote pseudo cosine sequences of G. We say this pair of sequences is \it tight whenever s₀ p₀, s₁ p₁, ..., s_D p_D is a pseudo cosine sequence of G. In this paper, we determine all the tight pairs of pseudo cosine sequences of G.

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• Pseudo-distance-regularised graphs are distance-regular or distance-biregular
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