The Terwilliger algebra of the incidence graphs of Johnson geometry

Levstein and Maldonado [F. Levstein, C. Maldonado, The Terwilliger algebra of the Johnson schemes, Discrete Mathematics 307 (2007) 1621–1635] computed the Terwilliger algebra of the Johnson scheme $J(n,m)$ when $3m\le n$. In this paper, we determine the Terwilliger algebra of the incidence graph $J(n,m,m+1)$ of Johnson geometry when $3m\le n$, give two bases of this algebra, and calculate its dimension.