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arXiv · 1704.05673

Automorphism group of the subspace inclusion graph of a vector space

Dein Wong·Xinlei Wang·Fenglei Tian
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Abstract

In a recent paper [Comm. Algebra, 44(2016) 4724-4731], Das introduced the graph $\mathcal{I}n(\mathbb{V})$, called subspace inclusion graph on a finite dimensional vector space $\mathbb{V}$, where the vertex set is the collection of nontrivial proper subspaces of $\mathbb{V}$ and two vertices are adjacent if one is properly contained in another. Das studied the diameter, girth, clique number, and chromatic number of $\mathcal{I}n(\mathbb{V})$ when the base field is arbitrary, and he also studied some other properties of $\mathcal{I}n(\mathbb{V})$ when the base field is finite. In this paper, the automorphisms of $\mathcal{I}n(\mathbb{V})$ are determined when the base field is finite.

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Dein Wong, Xinlei Wang, Fenglei Tian. 2017-04-19. Automorphism group of the subspace inclusion graph of a vector space. https://arxiv.org/abs/1704.05673

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