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:
“The ability to secure an independent livelihood and honorable employ suited to her education and capacities is the only true foundation of the social elevation of woman, even in the very highest classes of society. While she continues to be educated only to be somebody’s wife, and is left without any aim in life till that somebody either in love, or in pity, or in selfish regard at last grants her the opportunity, she can never be truly independent.”
—Catherine E. Beecher (1800–1878)
“I have heard, in such a way as to believe it, of your recently saying that both the Army and the Government needed a Dictator. Of course it was not for this, but in spite of it, that I have given you the command. Only those generals who gain success, can set up dictators.”
—Abraham Lincoln (1809–1865)