This article is cited in 3 papers

Graph-links: nonrealizability, orientation, and Jones polynomial

D. P. Ilyutko^ab, V. S. Safina<sup>a

a</sup> Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, Moscow, Russia
^b Delone Laboratory of Discrete and Computational Geometry, P. G. Demidov Yaroslavl State University, Yaroslavl, Russia

Abstract: The present paper is devoted to graph-links with many components and consists of two parts. In the first part of the paper we classify vertices of a labeled graph according to the component they belong to. Using this classification, we construct an invariant of graph-links. This invariant shows that the labeled second Bouchet graph generates a nonrealizable graph-link.
In the second part of the work we introduce the notion of an oriented graph-link. We define a writhe number for the oriented graph-link and we get an invariant of oriented graph-links, the Jones polynomial, by normalizing the Kauffman bracket with the writhe number.

UDC: 515.16+519.17

 English version: Journal of Mathematical Sciences, 2016, 214:5, 632–664