Let G be the simple graph on the vertex set V(G) = {a, b, c, d, e, f} with adjacency matrix: 011101 101110 1 1 0 0 0 0 1 1 0 0 1 0 010100 A = 100000 where row 1 corresponds to vertex a, row 2 to vertex b, etc. Without drawing the graph G, use the adjacency matrix A to: (a) find the degree of each vertex of G. (b) find the number of edges in G. (c) explain why G has no 6-cycle. (d) find the number of paths in G of length 2, starting at vertex b. (e) find the number of walks of length 3 from vertex 6 to vertex a in G.

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