Independent Set

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An independent set S is a subset of V in G such that no two vertices in S are adjacent. I suppose that its name is meaning that vertices in an independent set S is independent on a set of edges in a graph G. Like other vertex sets in graph theory, independent set has maximal and maximum sets as follows:

The independent set S is maximal if S is not a proper subset of any independent set of G.
The independent set S is maximum if there is no other independent set has more vertices than S.
That is, a largest maximal independent set is called a maximum independent set. The maximum independent set problem is an NP-hard optimization problem.

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