Abstract
Let Γ be a distance-regular graph without induced subgraphsK2,1,1andr=max {j∣ (cj,aj,bj)= (c1,a1,b1)}. We give a necessary and sufficient condition for the existence of a strongly closed subgraph which is (cr+1+ar+1)-regular of diameterr+1 containing a given pair of vertices at distancer+1.
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