Distance-regular Subgraphs in a Distance-regular Graph, VI

In this paper we give a sufficient condition for the existence of a strongly closed subgraph which is (cq+aq)-regular of diameterqcontaining a given pair of vertices at distanceqin a distance-regular graph. Moreover we show that a distance-regular graph withr = max {j| (cj,aj,bj) = (c1,a1,b1)} ,bq − 1>bqandcq+r = 1 satisfies our sufficient condition.