Full automorphism group of the generalized symplectic graph

Abstract

Let $\mathbb{F}_q$ be a finite field of odd characteristic, m, ν the integers with 1 ⩽ m ⩽ ν and K a 2ν × 2ν nonsingular alternate matrix over $\mathbb{F}_q$. In this paper, the generalized symplectic graph GSp _2ν (q, m) relative to K over $\mathbb{F}_q$ is introduced. It is the graph with m-dimensional totally isotropic subspaces of the 2ν-dimensional symplectic space $\mathbb{F}_q^{(2v)}$ as its vertices and two vertices P and Q are adjacent if and only if the rank of PKQ ^T is 1 and the dimension of P ∩ Q is m − 1. It is proved that the full automorphism group of the graph GSp _2ν (q, m) is the projective semilinear symplectic group PΣp(2ν, q).