On a Distance-Regular Graph of Even Height with ke = kf

Abstract.

 Let Γ be a distance-regular graph of diameter d. The height of Γ is defined by h = max{j∣p ^d _d,j ≠ 0}. Let e, f be positive integers such that e < f and e + f≤d, and let d = 2e + s for some positive integer s. We show that if k _e = k _f , h≤ 2s and the height h is even, then Γ is an antipodal 2-cover.