# The automorphism groups of some token graphs

## TL;DR

This paper determines the automorphism groups of certain token graphs, including path graphs, cycles, stars, fans, and wheel graphs, revealing their symmetries and structural properties.

## Contribution

It provides the first explicit descriptions of automorphism groups for these specific token graphs, expanding understanding of their symmetry structures.

## Key findings

- Automorphism group of the k-token graph of P_n for n ≠ 2k is characterized.
- Automorphism groups of 2-token graphs for cycle, star, fan, and wheel graphs are determined.
- Results reveal symmetry properties of token graphs related to classical graph families.

## Abstract

In this paper we obtain the automorphism groups of the token graphs of some graphs. In particular we obtain the automorphism group of the $k$-token graph of the path graph $P_n$, for $n\neq 2k$. Also, we obtain the automorphism group of the $2$-token graph of the following graphs: cycle, star, fan and wheel graphs.