A bipartite graph with partite sets U and W is called balanced if |U| = |W|. Let G be a regular bipartite graph with at least one edge. Prove that G is balanced.
A regular graph means that every vertex has the same degree this implys that (using the bipartite property) the number of vertices in U = W again by it being bi partite and having vertices of equal degree implys that |U| = |W|.
At least in my head that makes sense any hint how to prove it?