Untitled

Abstract

To each weighted graph F, two invariants, a polynomial Pf(x,y, z) and the signature rj(r), are defined. The various partial degress of Pr(x,y, z) and c(T) are expressed in terms of maximal spanning graphs of T. Furthermore, one unexpected property of Tutte's dichromate is proved. These results are applied to knots or links in S3 .