On subspace inclusion graph of a vector space

Abstract

In this paper, we continue the study of the subspace inclusion graph on a finite-dimensional vector space with dimension n where the vertex set is the collection of non-trivial proper subspaces of a vector space and two vertices are adjacent if one is contained in other. It is shown that is perfect and non-planar. Moreover, a necessary and sufficient condition is provided for to be Eulerian. For , it is shown that is bipartite, vertex and edge-transitive and has a perfect matching. We also provide exact value of the independence number and bounds on the domination number of for .