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The Tutte polynomial and its applications. (English) Zbl 0769.05026
Matroid applications, Encycl. Math. Appl. 40, 123-225 (1992).
[For the entire collection see Zbl 0742.00052.]
A function $$f$$ on the class of all matroids is an isomorphism invariant if $$f(M)=f(N)$$ whenever $$M\cong N$$. For every element $$e$$ of $$M$$ define $$f(M)=f(M\backslash e)+f(M/e)$$ if $$e$$ is neither a loop nor an isthmus (where $$\backslash$$ and / stand for deletion and for contraction, respectively) and $$f(M)=f(M(e))f(M\backslash e)$$ otherwise. Such a function $$f$$ is a Tutte-Grothendieck invariant.
Such and more general invariants are presented with relations to graph colouring, flows and coding theory.

##### MSC:
 05B35 Combinatorial aspects of matroids and geometric lattices