# Automorphisms of the subspace sum graphs on a vector space

## TL;DR

This paper fully characterizes the automorphisms of the subspace sum graph on a finite-dimensional vector space, extending previous structural studies by providing a complete description of its symmetries.

## Contribution

It offers the first complete characterization of automorphisms of the subspace sum graph, a problem left open in prior research.

## Key findings

- Automorphisms are fully characterized.
- The structure of the automorphism group is described.
- Results extend understanding of the graph's symmetries.

## Abstract

The subspace sum graph $\mathcal{G}(\mathbb{V})$ on a finite dimensional vector space $\mathbb{V}$ was introduced by Das [Subspace Sum Graph of a Vector Space, arXiv:1702.08245], recently. The vertex set of $\mathcal{G}(\mathbb{V})$ consists of all the nontrivial proper subspaces of $\mathbb{V}$ and two distinct vertices $W_1$ and $W_2$ are adjacent if and only if $W_1+W_2=\mathbb{V}$. In that paper, some structural indices (e.g., diameter, girth, connectivity, domination number, clique number and chromatic number) were studied, but the characterization of automorphisms of $\mathcal{G}(\mathbb{V})$ was left as one of further research topics. Motivated by this, we in this paper characterize the automorphisms of $\mathcal{G}(\mathbb{V})$ completely.