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arXiv · 2310.00251

Direct sum graph of the subspaces of a finite dimensional vector space over finite fields

Bilal A. Wani·Aaqib Altaf·S. Pirzada·T. A. Chishti
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Abstract

In this paper, we introduce a new graph structure, called the $direct~ sum ~graph$ on a finite dimensional vector space. We investigate the connectivity, diameter and the completeness of $Γ_{U\oplus W}(\mathbb{V})$. Further, we find its domination number and independence number. We also determine the degree of each vertex in case the base field is finite and show that the graph $Γ_{U\oplus W}(\mathbb{V})$ is not Eulerian. We also show that under some mild conditions the graph $Γ_{U\oplus W}(\mathbb{V})$ is triangulated. We determine the clique number of $Γ_{U\oplus W}(\mathbb{V})$ for some particular cases. Finally, we find the size, girth, edge-connectivity and the chromatic number of $Γ_{U\oplus W}(\mathbb{V})$.

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Bilal A. Wani, Aaqib Altaf, S. Pirzada, T. A. Chishti. 2023-09-30. Direct sum graph of the subspaces of a finite dimensional vector space over finite fields. https://arxiv.org/abs/2310.00251

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