Bipartition Polynomials, the Ising Model, and Domination in Graphs

• Autorzy: Markus Dod , Tomer Kotek , James Preen , Peter Tittmann
• Języki publikacji: EN

Abstrakty

EN

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. We apply this approach to show that, analogously to the Tutte polynomial, the Ising polynomial introduced by Andrén and Markström in [3], can be represented as a sum over spanning forests.

Słowa kluczowe

EN

domination; Ising model; graph polynomial

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2015
• Tom: 35
• Numer: 2
• Strony: 335-353

Daty

wydano

2015-05-01

otrzymano

2014-01-23

poprawiono

2014-09-16

zaakceptowano

2014-09-16

online

2015-04-18

Twórcy

autor

Markus Dod

• Faculty Mathematics, Sciences, Computer Science University of Applied Sciences Mittweida

autor

Tomer Kotek

• Institut für Informationssysteme 184/4 Technische Universität Wien, Vienna, Austria

autor

James Preen

• Mathematics Cape Breton University Sydney, Canada

autor

Peter Tittmann

• Faculty Mathematics, Sciences, Computer Science University of Applied Sciences Mittweida

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1808