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arXiv · 1510.02046

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

Angsuman Das
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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 $\Gamma(\mathbb{V})$.

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Angsuman Das. 2015-10-06. On Non-Zero Component Graph of Vector Spaces over Finite Fields. https://doi.org/10.1142/s0219498817500074

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