An inequality for regular near polygons

2003/12/07 by Paul Terwilliger, Terwilliger, Paul, Chih-wen Weng +1
Engineering · Mathematics · #05E30 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #graph theory and CDMA systems #math.CO #msc:05E30

paper · pdf · doi:10.48550/arxiv.math/0312149

13 pages

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

Abstract

Let G denote a near-polygon distance-regular graph with diameter d≥ 3, valency k and intersection numbers a₁>0, c₂>1. Let θ₁ denote the second largest eigenvalue for the adjacency matrix of G. We show θ₁ is at most (k-a₁-c₂)/(c₂-1). We show the following are equivalent: (i) Equality is attained above; (ii) G is Q-polynomial with respect to θ₁; (iii) G is a dual polar graph or a Hamming graph.

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