On Q-polynomial distance-regular graphs Γ with strongly regular graphs ΓSUB2/SUB and ΓSUB3/SUB

摘要

Let ?? be a distance-regular graph of diameter 3 with stronglyregular graphs ??2 and ??3. Then ?? has intersection array ft(c2 + 1) +a3; tc2; a3 + 1; 1; c2; t(c2 + 1)g (Nirova M.S.) If ?? is Q-polynomial theneither a3 = 0; t = 1 and ?? is Taylor graph or (c2 + 1) = a3(a3 + 1)=(t2 ??a3 ?? 1). We found 4 infinite series feasible intersection arrays in thissituation.