Geodesic
Thin distance-regular graphs with classical parameters \((D, q, q, \frac{q^t-1}{q-1}-1)\) with \(t> D\) are the Grassmann graphs
The electronic journal of combinatorics, Tome 28 (2021) no. 4
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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.
DOI : 10.37236/10586
Classification : 05C50, 05C12, 05C75, 05E30
Mots-clés : Delsarte clique, Terwilliger algebra 
@article{10_37236_10586,
     author = {Xiaoye Liang and Ying-Ying Tan and Jack Koolen},
     title = {Thin distance-regular graphs with classical parameters {\((D,} q, q, \frac{q^t-1}{q-1}-1)\) with \(t> {D\)} are the {Grassmann} graphs},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {4},
     doi = {10.37236/10586},
     zbl = {1486.05180},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10586/}
}
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Xiaoye Liang; Ying-Ying Tan; Jack Koolen. Thin distance-regular graphs with classical parameters \((D, q, q, \frac{q^t-1}{q-1}-1)\) with \(t> D\) are the Grassmann graphs. The electronic journal of combinatorics, Tome 28 (2021) no. 4. doi: 10.37236/10586

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