Nonisotropic symplectic graphs over finite commutative rings

Abstract

In this paper, we study two types of nonisotropic symplectic graphs over finite commutative rings defined by nonisotropic free submodules of rank 2 and McCoy rank of matrices. We prove that the graphs are quasi-strongly regular or Deza graphs and we find their parameters. The diameter and vertex transitivity are also analyzed. Moreover, we study subconstituents of these nonisotropic symplectic graphs.

Keywords

• local ring
• mccoy rank
• nonisotropic subspace
• symplectic space