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Bipartition Polynomials, the Ising Model, and Domination in Graphs

Markus DodTomer KotekJames PreenPeter Tittmann — 2015

Discussiones Mathematicae Graph Theory

This paper introduces a trivariate graph polynomial that is a common generalization of the domination polynomial, the Ising polynomial, the matching polynomial, and the cut polynomial of a graph. This new graph polynomial, called the bipartition polynomial, permits a variety of interesting representations, for instance as a sum ranging over all spanning forests. As a consequence, the bipartition polynomial is a powerful tool for proving properties of other graph polynomials and graph invariants....

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