5. Let the sequence of numbers g0, g1, ... ,,be defined by g0 = 0, g1 = 1, and, for every n ＞ 1, . Solve in terms of n, by the method of generating functions.

6. The girth of a graph G is the length of the shortest cycle in G. Let G be a simple graph with y vertices, e edges, and girth g. It is known that if G is planar, then e . Let K5 be a complete graph with 5 vertices, K5and K3,3 be a complete bipartite graph with 3 vertices in each partition. Draw Ks and K3,3, and show that they are not planar.

5. Let the sequence of numbers g₀, g₁, ... ,,be defined by g₀ = 0, g₁ = 1, and, for every n ＞ 1, . Solve in terms of n, by the method of generating functions.

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