A Tutte polynomial for signed graphs
A signed graph is an undirected graph whose edges are labelled by plus and minus signs. A Tutte polynomial is a certain polynomial assigned to such a graph and analogous to the chromatic polynomial. To a given planar the so-called medial graph is assigned; its embedding in the plane is called a universe. The universes are then transferred into link diagrams; they can be regarded as links and knots in the 3-dimensional space. In such a way topological problems concerning curves and knots may be studied by means of graphs, using the mentioned concepts of the signed graph and the Tutte polynomial.
scientific article; zbMATH DE number 4144001
scientific article