Geodesic
Graph-links: nonrealizability, orientation, and Jones polynomial
Contemporary Mathematics. Fundamental Directions, Topology, Tome 51 (2013), pp. 33-63

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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. 
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     author = {D. P. Ilyutko and V. S. Safina},
     title = {Graph-links: nonrealizability, orientation, and {Jones} polynomial},
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D. P. Ilyutko; V. S. Safina. Graph-links: nonrealizability, orientation, and Jones polynomial. Contemporary Mathematics. Fundamental Directions, Topology, Tome 51 (2013), pp. 33-63. http://geodesic.mathdoc.fr/item/CMFD_2013_51_a2/