Tutte–Grothendieck invariant
In mathematics, a Tutte–Grothendieck (TG) invariant is a type of graph invariant that satisfies a generalized deletion–contraction formula. Any evaluation of the Tutte polynomial would be an example of a TG invariant. Definition A graph function f is TG-invariant if: Above G / e denotes edge contraction whereas G \ e denotes deletion. The numbers c, x, y, a, b are parameters. Generalization to matroids The matroid function f is TG if: It can be shown that f is given by: where E is the edge set of M; r is the rank function; and is the generalization of the Tutte polynomial to matroids. Grothendieck group The invariant is named after Alexander Grothendieck because of a similar construction of the Grothendieck group used in the Riemann–Roch theorem. For more details see: References Graph invariants