Abstract
Abstract : Consider a simple graph whose vertices are s-dimensional subspaces of a d-dimensional vector space V over (GF(q). Two vertices in this graph are adjacent if the corresponding s-dimensional subspaces intersect in an (s-1)-dimensional subspace. This graph will be called an (s,q,d)-projective graph. The Theorem 1 of this paper can be used to obtain a characterization of the (s,q,d)-projective graphs provided d is larger than some function of s and q. Characterization problems of Affine spaces and Polar spaces are also concerned in terms of flats of higher dimensions.
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