On the graphical characterization of the projective space over a finite field

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We shall construct the graphs whose vertex set is the set of all k-dimension projective subspaces of PG(n, q), two vertices being joined by an edge whenever they have a (k 1 )-dimension projective subspace in common. Then these graphs satisfy the condition (ii), and for two vertices c1 and B, with d(cr, /I) = 2, d(cr)nd(/?) is isomorphic to L,(t). (d is a distance function.) I received the advice that Theorem A is generalized by applying the main theorem of Cohen [4] as follows: 143 0095-8956/85 $3.00

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