A new characterization of the dual polar graphs

2017/11/16 by Zhi Qiao, Qiao, Zhi, Jack H. Koolen +1
Chemistry · Mathematics · #05C50 #05C75 #05E30 #Combinatorics (math.CO) #FOS: Mathematics #Ferrocene Chemistry and Applications #Finite Group Theory Research #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1711.05874

openalex publication_date 2017/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give a new characterization of the dual polar graphs, extending the work of Brouwer and Wilbrink on regular near polygons. Also as a consequence of our characterization we confirm a conjecture of the authors on non-bipartite distance-regular graphs with smallest eigenvalue at most -k/2, where k is the valency of the distance-regular graph, in case of c₂ ≥3 and a₁ =1.

Related

• An inequality for regular near polygons
• Light tails and the Hermitian dual polar graphs
• Distance-regular graphs with valency k having smallest eigenvalue at most -k/2
• Non-bipartite distance-regular graphs with a small smallest eigenvalue
• Computations regarding certain graphs associated to finite polar spaces