Writhe-like invariants of alternating links

It is known that the writhe calculated from any reduced alternating link diagram of same (alternating) has value. That is, it a invariant if we restrict ourselves to diagrams. This due fact diagrams are obtainable each other via flypes and do not change writhe. In this paper, introduce several quantities derived Seifert graphs We prove they “writhe-like” invariants, namely general but invariants when restricted The determination these elementary non-recursive so easy calculate. demonstrate many different links can be easily distinguished by new even for large, complicated knots which such as Jones polynomial hard compute. As an application, also derive only condition strongly invertible rational link.