Consider an undirected graph G = (V;E). An independent set is a subset I   V such that for any vertices i; j 2 I, there is no edge between i and j in E. A set i is a maximal independent set if no additional vertices of V can be added to I without violating its independence. Note, however, that a maximal independent sent is not necessarily the largest independent set in G. Let  (G) denote the size of the largest maximal independent set in G.   1) What is  (G) if G is a complete graph on n vertices? What if G is a cycle on n vertices?

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