Construction of a class of generalized symplectic graphs based on subspaces in symplectic space over finite fields

Abstract

Let F_q be a finite field of order q and F_q (2ν) be 2ν-dimensional symplectic space. In the present paper, we study the generalized symplectic graph Γ of type (m, 0, 1), whose vertex set is the set of m-dimensional totally isotropic subspaces of F (2ν) q , and for vertices X and Y , X ∼ Y if r(XKY^t ) = 0 and dim(X∩Y ) = m−1, where K = (0&I (ν)\\ −I (ν) &0 ). It is shown that Γ is vertex-transitive, and Γ is a 5-Deza graph with diameter m+ 1. Moreover, we determine the parameters concerning the first subconstituent Γ_1 and it is shown that Γ1 is also a 5-Deza graph.