polynomial is an ambient isotopy invariant for spatial graphs with vertices of degree at most 3. However, for other spatial graphs it is only a regular isotopy invariant. It is convenient to use because it can be computed using skein relations. Also, the Yamada polynomial can be used to detect whether a spatial graph with vertices of degree at most 3 is chiral (i.e., distinct from its mirror image). The Yokota polynomial is an ambient isotopy invariant for all spatial graphs that reduces to the Yamada polynomial for graphs with vertices of degree at most 3. However, the Yokota polynomial is more difficult to compute, and cannot be used to show that a spatial graph is chiral.

In a lecture in 1990, Jon Simon introduced an invariant of embeddings of the graphs $K_5$ and $K_{3,3}$ with labeled vertices in $S^3$. The Simon invariant is easy to compute from a projection of an embedding and has been useful in obtaining results about embeddings of non-planar graphs [@Huh; @Nikkuni; @2006a; @Nikkuni; @2006; @Nikkuni; @2009; @Nikkuni; @2009b; @Ohyama; @Shinjo; @Taniyama; @1994; @Taniyama; @1995]. In 1995, Taniyama [@Taniyama; @1995] showed that the Simon invariant is a special case of a cohomology invariant for all 