Geodesic
Linear embeddings of simple graphs in $\mathbb R^3$
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 27-34 Cet article a éte moissonné depuis la source Math-Net.Ru

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Our problem is to classify for any simple graph all linear embeddings of the graph in $\mathbb R^3$ up to rigid isotopy. We solve the problem for graphs with at most five vertices. For graphs with more than five vertices, we give lower and upper bounds for the number of rigid isotopy classes of linear embeddings in $\mathbb R^3$. Bibl. – 3 titles. 
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     title = {Linear embeddings of simple graphs in~$\mathbb R^3$},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a2/}
}
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E. N. Glushak. Linear embeddings of simple graphs in $\mathbb R^3$. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 27-34. http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a2/

[1] J. A. Calvo, “The embedding space of hexagonal knots”, Topology and its Applications, 112 (2001), 137–174 | DOI | MR | Zbl

[2] J. A. Calvo, “Geometric knot spaces and polygonal isotopy”, J. Knot Theory Ramif., 10 (2001), 245–267 | DOI | MR | Zbl

[3] E. N. Glushak, “Lineinye vlozheniya polnykh grafov s pyatyu vershinami”, Materialy Vseros. nauch.-metod. konf., Velikii Novgorod, 2004, 31–34