# A characterization of the Grassmann graphs

## Seminar/Forum

Room 107
Peter Hall

Building on other people's work Metsch showed in the 1990's that the Grassmann graph $$Jq(n, D)$$ is characterized as a distance-regular graph when $$n \geq 2D + 2 + \max(4-q, 0)$$ and $$D \geq 3$$. Van Dam and Koolen constructed the twisted Grassmann graph with the same intersection numbers as the Grassmann graph $$Jq(2D+1,D)$$.
In this talk we will show that $$J_q(2D, D)$$ is characterized as a distance-regular graph if $$D$$ is large enough.