Strongly Closed Subgraphs in a Distance-Regular Graph with c 2 > 1.

Let Γ be a distance-regular graph of diameter d ≥ 3 with c 2 > 1. Let m be an integer with 1 ≤ m ≤ d − 1. We consider the following conditions: Suppose that the condition ( SC) m holds. Then it has been known that the condition ( BB) i holds for all i with 1 ≤ i ≤ m. Similarly we can show that the condition ( CA) i holds for all i with 1 ≤ i ≤ m. In this paper we prove that if the conditions ( BB) i and ( CA) i hold for all i with 1 ≤ i ≤ m, then the condition ( SC) m holds. Applying this result we give a sufficient condition for the existence of a dual polar graph as a strongly closed subgraph in Γ. [ABSTRACT FROM AUTHOR]