基于Ising分拆函数的Bethe近似的新的图多项式
New graph polynomials from the Bethe approximation of the Ising partition function
摘要：
引入了两个图多项式并讨论了它们的性质。一个是两个变量的多项式，其调查的动机是由Ising分拆函数的Bethe近似的性能分析。另一个是一个变量的多项式，它是通过第一个变量的特殊化得到的。证明了这些多项式满足删缩关系，是Tutte（1947，Proc. Cambridge Philos.Soc.43，26-40）提出的V函数的新例子。对于这些多项式，我们讨论了特殊值的解释，然后得到了子核心图的数量上界，即，没有1度顶点的生成子图。证明了单变量多项式等于单-二聚体分拆函数，配分函数的权重由该变量参数化。讨论了该多项式系数的性质和可能的零点区域。
英文摘要：
We introduce two graph polynomials and discuss their properties. One is a polynomial of two variables whose investigation is motivated by the performance analysis of the Bethe approximation of the Ising partition function. The other is a polynomial of one variable that is obtained by the specialization of the first one. It is shown that these polynomials satisfy deletion-contraction relations and are new examples of the V-function, which was introduced by Tutte (1947, Proc. Cambridge Philos. Soc. 43, 26-40). For these polynomials, we discuss the interpretations of special values and then obtain the bound on the number of sub-coregraphs, i.e., spanning subgraphs with no vertices of degree one. It is proved that the polynomial of one variable is equal to the monomer-dimer partition function with weights parameterized by that variable. The properties of the coefficients and the possible region of zeros are also discussed for this polynomial.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
