An inequality for regular near polygons

Paul Terwilliger*, Chih-wen Weng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Let Γ 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 of Γ. We show θ1≤k-a1-c2/c2-1. We show the following (i)-(iii) are equivalent. (i) Equality is attained above; (ii) Γ is Q-polynomial with respect to θ1; (iii) Γ is a dual polar graph or a Hamming graph.

Original languageEnglish
Pages (from-to)227-235
Number of pages9
JournalEuropean Journal of Combinatorics
Issue number2
StatePublished - 1 Feb 2005


  • Distance-regular graph
  • Dual polar graph
  • Hamming graph
  • Near polygon
  • Q-polynomial


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