DISTANCE-REGULAR GRAPHS WITH B(T)=1 AND ANTIPODAL DOUBLE-COVERS

摘要

Let Gamma be a distance-regular graph of diameter d and valency k > 2. If b(t) = 1 and 2t less than or equal to d, then Gamma is an antipodal double-cover. Consequently, if f > 2 is the multiplicity of an eigenvalue of the adjacency matrix of Gamma and if Gamma is not an antipodal double-cover then d less than or equal to 2f - 3. This result is an improvement of Godsil's bound. (C) 1996 Academic Press, Inc. [References: 12]