Full automorphism group of the generalized symplectic graph

Let Fq be a finite field of odd characteristic, m, v the integers with 1 ≤ m ≤ v and K a 2v × 2v nonsingular alternate matrix over Fq. In this paper, the generalized symplectic graph GSp2v（q, m） relative to K over Fq is introduced. It is the graph with m-dimensional totally isotropic subspaces of the 2v-dimensional symplectic space Fq（2v） as its vertices and two vertices P and Q are adjacent if and only if the rank of PKQw is 1 and the dimension of P ∩ Q is m - 1. It is proved that the full automorphism group of the graph GSp2v（q, m） is the projective semilinear symplectic group P∑p（2v, q）.