A new characterization of the dual polar graphs

TL;DR

This paper introduces a novel characterization of dual polar graphs, extending prior work on near polygons and confirming a conjecture about non-bipartite distance-regular graphs with specific eigenvalue properties.

Contribution

It provides a new characterization of dual polar graphs and verifies a conjecture related to eigenvalues in certain non-bipartite distance-regular graphs.

Findings

New characterization of dual polar graphs

Confirmation of a conjecture on eigenvalues of distance-regular graphs

Extension of work on regular near polygons

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 $c_2 \geq3$ and $a_1 =1$.