Distance-regular subgraphs in a distance-regular graph .4.

Let Gamma be a distance-regular graph with a(1) > 0, r = max{j \ (c(j), a(j), b(j)) = (c(1), a(1), b(1))} greater than or equal to 2 and a(i) = a(1)c(i), for 1 less than or equal to i less than or equal to 2r. Take any u and v in Gamma at distance r + 1. We show that there exists a collinearity graph of a generalized 2(r + 1)-gon of order (a(1) + 1, c(r+1) - 1) containing u and v as a subgraph in Gamma. (C) 1997 Academic Press Limited.