The Terwilliger algebra of Odd graphs

In [F. Levstein, C. Maldonado, The Terwilliger algebra of the Johnson schemes, Discrete Math. 307 (2007) 1621–1635], Levstein and Maldonado computed the Terwilliger algebra of the Johnson scheme J(n,m)J(n,m) when 3m≤n3m≤n. The distance-mm graph of J(2m+1,m)J(2m+1,m) is the Odd graph Om+1Om+1. In this paper, we determine the Terwilliger algebra of Om+1Om+1 and give its basis.