Independent Set (graph Theory)
In graph theory, an independent set or stable set is a set of vertices in a graph, no two of which are adjacent. That is, it is a set I of vertices such that for every two vertices in I, there is no edge connecting the two. Equivalently, each edge in the graph has at most one endpoint in I. The size of an independent set is the number of vertices it contains.
A maximal independent set is an independent set such that adding any other vertex to the set forces the set to contain an edge.
A maximum independent set is a largest independent set for a given graph G and its size is denoted α(G). The problem of finding such a set is called the maximum independent set problem and is an NP-hard optimization problem. As such, it is unlikely that there exists an efficient algorithm for finding a maximum independent set of a graph.
Read more about Independent Set (graph Theory): Properties, Finding Independent Sets, Software For Searching Maximum Independent Set, Software For Searching Maximal Independent Set
Famous quotes containing the words independent and/or set:
“Nevertheless, in the Lord woman is not independent of man or man independent of woman. For just as woman came from man, so man comes through woman; but all things come from God.”
—Bible: New Testament, 1 Corinthians 11:11.
In v. 9, Paul wrote “Neither was man created for woman, but woman for man.”
“A fool, A fool! I met a fool i’ the forest,
A motley fool. A miserable world!
As I do live by food, I met a fool,
Who laid him down and basked him in the sun,
And railed on Lady Fortune in good terms,
In good set terms, and yet a motley fool.”
—William Shakespeare (1564–1616)