Let $m, n \in \mathbb{N}$ with $m \ne n$. Determine the automorphism group of the complete bipartite
Graph $\mathcal{V}\_{m,n}$.

Some definitions:
A complete bipartite graph is a special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set.

A bipartite graph is a graph whose vertices can be divided into two disjoint and independent sets $U$ and $V$, that is every edge connects a vertex in $U$ to one in $V$. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles.

My idea: In need to find an appropriate characterization of the larger set in the bipartite decomposition, but I am not sure.

An old exam question I am looking at to learn for my upcoming discrete math exam. I unfortunately am not sure what to do. Thanks in advance!