On Non-Zero Component Graph of Vector Spaces over Finite Fields

Abstract

In this paper, we study non-zero component graph $\Gamma (\mathbb{V})$ on a finite dimensional vector space $\mathbb{V}$ over a finite field $\mathbb{F}$. We show that the graph is Hamiltonian and not Eulerian. We also characterize the maximal cliques in $\Gamma (\mathbb{V})$ and show that there exists two classes of maximal cliques in $\Gamma (\mathbb{V})$. We also find the exact clique number of $\Gamma (\mathbb{V})$ for some particular cases. Moreover, we provide some results on size, edge-connectivity and chromatic number of $\Gamma (\mathbb{V})$.

10 pages, 3 figures

References in corpus (1)

• Results on the intersection graphs of subspaces of a vector space

Cited by in corpus (4)

• Non-Zero Component Graph of a Finite Dimensional Vector Space
• Subspace Sum Graph of a Vector Space
• On Perfectness of Intersection Graph of Ideals of ${\mathbb{Z}}_n$
• Leibniz algebras and graphs