On invariants of graphs with applications to knot theory

To each weighted graph Γ, two invariants, a polynomial P Γ (x,y,z) and the signature σ(Γ), are defined. the various partial degress of P Γ (x,y,z) and σ(Γ) are expressed in terms of maximal spanning graphs of Γ. Furthermore, one unexpected property of Tutte's dichromate is proved. These results are applied to knots or links in S 3

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