English

Automorphism group of the subspace inclusion graph of a vector space

Combinatorics 2017-04-20 v1

Abstract

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

Keywords

Cite

@article{arxiv.1704.05673,
  title  = {Automorphism group of the subspace inclusion graph of a vector space},
  author = {Dein Wong and Xinlei Wang and Fenglei Tian},
  journal= {arXiv preprint arXiv:1704.05673},
  year   = {2017}
}

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10 pages