Thin Distance-Regular Graphs with Classical Parameters $(D,q,q, \frac{q^{t}-1}{q-1}-1)$ with $t> D$ are the Grassmann Graphs

Author:

Tan Ying Ying,Liang Xiaoye,Koolen Jack

Abstract

In the survey paper by Van Dam, Koolen and Tanaka (2016), they asked to classify the thin $Q$-polynomial distance-regular graphs. In this paper, we show that a thin distance-regular graph with the same intersection numbers as a Grassmann graph $J_q(n, D)~ (n \geqslant 2D)$ is the Grassmann graph if $D$ is large enough.

Publisher

The Electronic Journal of Combinatorics

Subject

Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics

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