P and Q polynomial schemes with q = −1

AbstractA theorem of D. Leonard, as it appears in Bannai and Ito (Benjamin-Cummings Lecture Note Series, No. 58, Menlo Park, Ca., 1984), says the intersection numbers of distance-regular graphs with the Q-polynomial property take seven possible forms, called 1, 1A, 2, 2A, 2B, 2C, and 3. In this paper we show the known list of examples of type 3 is complete