Question: 3. A bipartite graph (X, Y, E) has |X| = |Y| = n and is rregatar: every vertex {in X or in Y) is the

3. A bipartite graph (X, Y, E) has |X| = |Y| = n and is rregatar: every vertex {in X or in Y) is the endpoint of exactly r edges. (a) Determine |E|, the number of edges in the graph. (b) Show that any vertex cover must contain at least n vertices. (This implies that there is a matching ofsize a, which matches every vertex in X to a vertex in Y. ,1

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