Let G be a bipartite graph with vertex partition { V_1, V_2}.

a)Prove that:

 \sum_{x \exists V_1}\deg(x) = |E| = \sum_{y \exists V_2}\deg(y)


b) A graph is k-regular if every vertex has degree k. Prove that if G is k-regular with  k > 0 , then |V_1| = |V_2| (NOTE: G is bipartite with vertex partition { V_1, V_2}.)