3-bounded property in a triangle-free distance-regular graph

TL;DR

This paper proves that certain triangle-free distance-regular graphs with specific parameters are 3-bounded, extending understanding of their structural properties in algebraic combinatorics.

Contribution

It establishes the 3-bounded property for a class of triangle-free distance-regular graphs with classical parameters, under specific intersection number conditions.

Findings

Proves the 3-bounded property for these graphs

Extends previous results on distance-regular graphs

Provides new insights into graph structure based on parameters

Abstract

Let $\Gamma$ denote a distance-regular graph with classical parameters $(D, b, \alpha, \beta)$ and $D\geq 3$. Assume the intersection numbers $a_1=0$ and $a_2\not=0$. We show $\Gamma$ is 3-bounded in the sense of the article [D-bounded distance-regular graphs, European Journal of Combinatorics(1997)18, 211-229].