An independent set in a graph is a subset of the vertices, no two of which are adjacent. The maximum independent set is the largest such subset. A Maximal Independent Set of a graph G=(V, E) is an independent set M such that the addition to M of any vertex in V-M creates a non-independent set. Write an efficient algorithm to find a maximal independent set in a graph. Demonstrate a graph on which your algorithm's maximal independent set is not a maximum independent set.