The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a polynomial in two variables which plays an important role in graph theory, a branch of mathematics and theoretical computer science. It is defined for every undirected graph and contains information about how the graph is connected. The importance of the Tutte polynomial comes from the information it contains about .
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Chromatic polynomial
The chromatic polynomial is a polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a function of the number of colors and was originally defined by George David Birkhoff to attack the four color problem. It was generalised to the Tutte polynomial by H. Whitney and W. T. Tutte, linking it to the Potts model of statistical physics.
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Potts model
In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice. By studying the Potts model, one may gain insight into the behaviour of ferromagnets and certain other phenomena of solid-state physics.
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Partition function (mathematics)
The partition function or configuration integral, as used in probability theory, information science and dynamical systems, is an abstraction of the definition of a partition function in statistical mechanics. It is a special case of a normalizing constant in probability theory, for the Boltzmann distribution.
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Graph property
In graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations such as particular labellings or drawings of the graph.
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Statistical physics
Statistical physics is the branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature. Its applications include many problems in the fields of physics, biology, chemistry, neurology, and even some social sciences, such as sociology.
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Spanning tree
In the mathematical field of graph theory, a spanning tree T of a connected, undirected graph G is a tree composed of all the vertices and some (or perhaps all) of the edges of G. Informally, a spanning tree of G is a selection of edges of G that form a tree spanning every vertex. That is, every vertex lies in the tree, but no cycles (or loops) are formed. On the other hand, every bridge of G must belong to T.
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Isomorphism
In abstract algebra, an isomorphism is a bijective homomorphism. Two mathematical structures are said to be isomorphic if there is an isomorphism between them. In category theory, an isomorphism is a morphism f: X → Y in a category for which there exists an "inverse" f: Y → X, with the property that both ff = idX and f f = idY.
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