# Automorphism group of the subspace inclusion graph of a vector space

## TL;DR

This paper determines the automorphism group of the subspace inclusion graph of a finite-dimensional vector space over a finite field, extending previous work on its structural properties.

## Contribution

It explicitly characterizes all automorphisms of the subspace inclusion graph for finite fields, a novel result in the study of these graphs.

## Key findings

- Automorphism group explicitly determined
- Structural properties of the graph analyzed
- Extension of previous results to automorphisms

## 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.