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 ) when 3 m ≤ n . The distance- m graph of J ( 2 m + 1 , m ) is the Odd graph O m + 1 . In this paper, we determine the Terwilliger algebra of O m + 1 and give its basis.