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:
“In the great department store of life, baseball is the toy department.”
—Los Angeles Sportscaster. quoted in Independent Magazine (London, Sept. 28, 1991)
“When you have come into the land that the LORD your God is giving you, and have taken possession of it and settled in it, and you say, “I will set a king over me, like all the nations that are around me,” you may indeed set over you a king whom the LORD your God will choose. One of your own community you may set as king over you; you are not permitted to put a foreigner over you, who is not of your own community.”
—Bible: Hebrew, Deuteronomy 17:14,15.