Suppose G is a graph with vertices a, b, c, d, e, f with adjacency matrix 1 0 1 0 0 0 0 1 1 1 [0 1 0 1 0 0 0 1 1 1 0 0 1 0 0 11 10 1 0 1 1 0 1 0 (where alphabetical order is used to determine the rows and columns of the adja- cency matrix). Find (a) the number of vertices in G (b) the number of edges in G (c) the degree of each vertex (d) the number of loops (e) the length of the longest simple path in G (f) the number of components in G (g) the distance between vertex a and vertex c