Counting Unbranched Subgraphs
David Ruelle
IHES 91440 Bures sur Yvette France
DOI: 10.1023/A:1018690328814
Abstract
Given an arbitrary finite graph, the polynomial Q( z) = S F Ĩ U Z cardF Q(z) = ΣF \in U^{_{^{Z^{cardF} } } } associates a weight zcardF to each unbranched subgraph F of length cardF. We show that all the zeros of Q have negative real part.
Pages: 157–160
Keywords: counting polynomial; graph; unbranched subgraph
Full Text: PDF
References
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2. O.J. Heilmann and E.H. Lieb, “Theory of monomer-dimer systems,” Commun. Math. Phys. 25 (1972),190- 232; 27 (1972), 166.
3. T.D. Lee and C.N. Yang, “Statistical theory of equations of state and phase relations. II. Lattice gas and Ising model,” Phys. Rev. 87 (1952), 410-419.
4. G. Polya and G. Szeg\ddot o, Aufgaben und Lehrs\ddot atze aus der Analysis, Vol. 2, 3rd edition, Springer, Berlin, 1964.
5. D. Ruelle, “Extension of the Lee-Yang circle theorem,” Phys. Rev. Letters 26 (1971), 303-304.
6. D.J. Wagner, “Multipartition series,” S.I.A.M. J. Discrete Math. 9 (1996), 529-544.