dichromate polynomial | Tutte-Whitney polynomial

Let G be an undirected graph, and let i denote the cardinal number of the set of externally active edges of a spanning tree T of G, j denote the cardinal number of the set of internally active edges of T, and t_(i j) the number of spanning trees of G whose internal activity is i and external activity is j. Then the Tutte polynomial, also known as the dichromate or Tutte-Whitney polynomial, is defined by T(x, y) = sum t_(i j) x^i y^j (Biggs 1993, p. 100).

chromatic polynomial | flow polynomial | rank polynomial | Tutte matrix