The independence complex of a graph is a mathematical object describing the independent sets of the graph. Formally, the independence complex of an undirected graph G, denoted by I(G), is an abstract simplicial complex (that is, a family of finite sets closed under the operation of taking subsets), formed by the sets of vertices in the independent sets of G. Any subset of an independent set is itself an independent set, so I(G) is indeed closed under taking subsets.
Every independent set in a graph is a clique in its complement graph, and vice versa. Therefore, the independence complex of a graph equals the clique complex of its complement graph, and vice versa.
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The independencecomplex of a graph is a mathematical object describing the independent sets of the graph. Formally, the independencecomplex of an undirected...
Clique complexes, independencecomplexes, flag complexes, Whitney complexes and conformal hypergraphs are closely related mathematical objects in graph...
context of matroids and greedoids, abstract simplicial complexes are also called independence systems. An abstract simplex can be studied algebraically...
States; a complex containing Two Independence Square Independence Square, Independence Hall in Philadelphia, Pennsylvania, United States Independence Square...
Independence have played at Ramblewood Soccer Complex and Sportsplex at Matthews. The team's colors are navy, blue, and parchment. The independence wear...
The Declaration of Independence, formally titled The unanimous Declaration of the thirteen united States of America (in the engrossed version but also...
other. Equivalently, it is the matching complex of the (m, n)-complete bipartite graph, or the independencecomplex of the m-by-n rook's graph. For any two...
The Cinderella complex was first described by Colette Dowling, who wrote a book on women's fear of independence – an unconscious desire to be taken care...
Scottish independence (Scottish Gaelic: Neo-eisimeileachd na h-Alba; Scots: Scots unthirldom) is the idea of Scotland regaining its independence and once...
over to Dr. Harekrushna Mahatab in the year 1946. After India got its independence under the new framework the Prime Minister or Premier position of provincial...
The UK Independence Party (UKIP /ˈjuːkɪp/ YOO-kip) is a Eurosceptic, right-wing populist political party in the United Kingdom. The party reached its greatest...
of wars of independence (also called liberation wars). These wars may or may not have been successful in achieving a goal of independence. Lists of active...
Independence Hall is a historic civic building in Philadelphia, where both the United States Declaration of Independence and the United States Constitution...
weighs 171,860 lb (77,950 kg). Independence, then known as Explorer, was displayed at the Kennedy Space Center Visitor Complex atop cement pilings and secured...
the order of the terms in the sequence. This allows defining linear independence for a finite set of vectors: A finite set of vectors is linearly independent...
The Arcade Independence Square is a shopping complex in Colombo, Sri Lanka. Housed in a group of renovated buildings including the former Jawatta Lunatic...
Independence Memorial Hall (also known as Independence Commemoration Hall) is a national monument in Sri Lanka built for commemoration of the independence...
simplicial complexes, see simplicial homology. Homological connectivity was calculated for various spaces, including: The independencecomplex of a graph;...
A referendum on Scottish independence from the United Kingdom was held in Scotland on 18 September 2014. The referendum question was "Should Scotland be...
Judicial independence is the concept that the judiciary should be independent from the other branches of government. That is, courts should not be subject...
property, or downward-closedness. Another term for an independence system is an abstract simplicial complex. A pair ( V , I ) {\displaystyle (V,{\mathcal {I}})}...
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