Symplectic totally isotropic subspace inclusion graph

Abstract

Symplectic totally isotropic subspace inclusion graph on a finite-dimensional symplectic space is a graph whose vertices are all totally isotropic subspaces of and two distinct vertices are adjacent if and only if one is contained in other. In this paper, the diameter, girth, clique number, chromatic number of are studied. Furthermore, a necessary and sufficient condition is provided for to be Eulerian. It is shown that if two symplectic totally isotropic subspace inclusion graphs on symplectic space are isomorphic, then the two subspace inclusion graphs on corresponding vector space are also isomorphic. It is also shown that is non-planar.