The Invariant Of Generalized N-labeling Of Links

The invariant survey is always the core of the knot theory. In1850s, R. H. Fox and his part-ners addressed the property of tricoloring of links. It was generalized to module n-labeling. In2006Jozef H. Przytycki discussed the property general n-labeling and the number of n-labeling of links, meanwhile, he discovered the relation between the number of tricoloring of links and their Jones polynomial and Kauffman polynomial. In this paper, we get a new result, general n-labeling of oriented links by relaxing the limits of the labeling coefficients. Furthermore, we proof it preserves three R-moves, so it is an oriented link invariant. After that, we define the number of n-labeling under a group of given numbers (a, b, c) and the number of general n-labeling, both of which are proofed to be invariants of an oriented link.