Geometric and Pseudo-geometric graphs (q²+1,q+1,1)

Abstract

Let θ ₀ be a particular vertex of a strongly regular graph G with parameters v, n₁, p ₁₁ ¹ p ₁₁ ² . Let A be the adjacency matrix of G, and B the submatrix of A whose rows correspond to the vertices of G adjacent to θ ₀ and whose columns correspond to the vertices of G nonadjacent to θ ₀. Then the design D(θ ₀) with incidence matrix B has the parameters v'=n₁ b'=v-n₁-1, r'=n₁-p₁₁¹-1, k' = p ₁₁ ² . In this paper we study the connection between G and D(θ ₀) when the graph G is geometric or pseudo-geometric (q²+1,q+1,1).