The Invariant Of Knots And Links Under Mutation

The knot theory introduces many invariants of the knots,such as Jones polynomial,Hom?y polynomial,Conway polynomial and the span of the bracket polynomial and so on.This paper mostly introduces thedefination of the mutation of the knots,and under mutation Jones polynomial and Hom?y polynomial of theknots remain unchange.Specifically,the author through the research for the tricolorability of the knots undermutation gives the conclusion that label number model n of the rational alternating knots is an invariantunder mutation.