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- W1972342015 abstract "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." @default.
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- W1972342015 date "2009-08-26" @default.
- W1972342015 modified "2023-09-27" @default.
- W1972342015 title "New graph polynomials from the Bethe approximation of the Ising partition function" @default.
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- W1972342015 doi "https://doi.org/10.48550/arxiv.0908.3850" @default.
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