A note on subspace sum graph of vector spaces

Abstract

For a finite dimensional vector space over a field the subspace sum graph of denoted by is defined to be a simple undirected graph with vertex set as the set of all non-trivial proper subspace of and, for any two distinct vertices V1 and V2 are adjacent if and only if In this paper, we establish some inter-relationship between as a graph and as a vector space by the study of genus of subspace sum graph of vector spaces. In particular, we characterize the collection of all the vector spaces for which the subspace sum graph of is either planar, toroidal or bi-toroidal. Furthermore, we determine the independence number of for a vector space of dimension at most 5.

Keywords

• subspace sum graph
• vector space
• independence number
• graph embedding