Abstract
In 2013, Z. Cheng and H. Gao introduced the writhe polynomial of virtual knots by using coloring of Gauss diagrams and L. H. Kauffman introduced the affine index polynomial of virtual knots by using the Cheng coloring. In 2016, I introduced the zero polynomial of virtual knots, and in 2017, Z. Cheng generalized the writhe polynomial, the affine index polynomial and the zero polynomial. These invariants are obtained by defining the weight of a crossing for a virtual knot diagram suitably. We give a grading of virtual knots by using the weights of crossings. This reveals a relationship between virtual knots and we can get grade tree diagrams of virtual knots. It enables us to compare virtual knots with many crossings more easily.
Keywords
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