Problem 7 Suppose G and # are two graphs in Figure 8 p d U Figure 8: Graph G (left) and graph H (right). (a). [2 points] Construct AG (the adjacenty matrix of G) and A# (the adjacenty matrix of H), each with row and column labels a, b, ..., f (for G) and p, q, ..., u (for H), respectively. Write the matrices carefully with correct notation. No partial credits for wrong answer. (b). [2 points] Construct the adjacenty lists of G and H. Write the lists carefully. No partial credits for wrong answer. (c). [3 points] Determine whether graph # in Figure 8 is planar or not (i.e., whether # can be drawn without edges crossing or not). If so, redraw H so that no edges cross; otherwise, explain your answer mathematically. (d). [3 points] Determine whether G and H are isomorphic. Exhibit an isomorphism or provide a rigorous argument that none exist. If the graphs are isomorphic, show that we can rearrange the vertices of H so that AG = Ay, where Ay is the adjacenty matrix of # with a particular rows and columns relabeling.\fANSWER: ( c) Graph H is Indeed planar , this is one of the example to redraw the graph so it becomes planar P 5