Random triangulations of the plane
European Journal of Combinatorics
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
Almost all maps are asymmetric
Journal of Combinatorial Theory Series B
Contraction-deletion invariants for graphs
Journal of Combinatorial Theory Series B
Graphs determined by polynomial invariants
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
On Dependency Graphs and the Lattice Gas
Combinatorics, Probability and Computing
New graph polynomials from the bethe approximation of the ising partition function
Combinatorics, Probability and Computing
Distinguishing graphs by their left and right homomorphism profiles
European Journal of Combinatorics
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In this paper we discuss the two variable Ising polynomials in a graph theoretical setting. This polynomial has its origin in physics as the partition function of the Ising model with an external field. We prove some basic properties of the Ising polynomial and demonstrate that it encodes a large amount of combinatorial information about a graph. We also give examples which prove that certain properties, such as the chromatic number, are not determined by the Ising polynomial. Finally we prove that there exist large families of non-isomorphic planar triangulations with identical Ising polynomial.