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We give a necessary condition for two diagrams of 3-regular spatial graphs with the same underlying abstract graph G to represent isotopic spatial graphs. The test works by reading off the writhes of the knot diagrams coming from a collection of cycles in G in each diagram, and checking whether the writhe tuples differ by an element in the image of a certain map of Z-modules determined by G. We exemplify by using our result to distinguish, for each n 3, all elements in a certain infinite family of embeddings of the M\"obius ladder Mₙ into R³. We also connect these writhe tuples to a classical invariant of spatial graphs due to Wu and Taniyama.
Friedl et al. (Mon,) studied this question.