Define the graph Gn to have the 2n nodes a0, a1, . . . , an-1, b0, b1, . . . , bn-1 and the…

Define the graph Gn to have the 2n nodes a0, a1, . . . , an_1, b0, b1, . . . , bn_1 and the following edges. Each node ai , for i = 0, 1, . . . , n _ 1, is connected to the nodes bj and bk, where j = 2i mod n and k = (2i + 1) mod n For instance, the graph G4 has the following edges: (a0, b0), (a0, b1), (a1, b2), (a1, b3), (a2, b0), (a2, b1), (a3, b2), and (a3, b3). (a) Find a perfect matching for G4. (b) Find a perfect matching for G5. !! (c) Prove that for every n, Gn has a perfect matching.