Bipartition Polynomials, the Ising Model, and Domination in Graphs
Markus Dod, Tomer Kotek, James Preen, Peter Tittmann (2015)
Discussiones Mathematicae Graph Theory
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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...