On some properties of vector space based graphs

Abstract

In this paper, we study some problems related to subspace inclusion graph In⁡(V) and subspace sum graph G(V) of a finite-dimensional vector space V. Namely, we prove that In⁡(V) is a Cayley graph as well as Hamiltonian when the dimension of V is 3. We also find the exact value of independence number of G(V) when the dimension of V is odd. The above two problems were left open in previous works in the literature. Moreover, we prove that the determining numbers of In⁡(V) and G(V) are bounded above by 6. Finally, we study some forbidden subgraphs of these two graphs.