Construction of symplectic graphs by using 2-dimensional symplectic non-isotropic subspaces over finite fields

Abstract

In most extant studies, symplectic graphs are defined by 1-dimensional subspaces and their orthogonality. In this paper, the symplectic graph is defined by 2-dimensional non-isotropic subspaces and their intersection. The symplectic graph is shown to be a 4-Deza graph. While the first subconstituent is shown to be a 4-Deza graph when ν⩾3 and a 3-Deza graph when ν=2, the second subconstituent is not regular, and the third subconstituent is a 4-Deza graph except in the case ν=2, when it is empty.