We use the topological invariant of spatial graphs introduced by S. Yamada to find necessary conditions for a spatial graph to be periodic with a prime period. The proof of the main result is based on computing the Yamada skein algebra of the solid torus and then proving that it injects into the Kauffman bracket skein algebra of the solid torus.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm190-0-1,
author = {Nafaa Chbili},
title = {Skein algebras of the solid torus and symmetric spatial graphs},
journal = {Fundamenta Mathematicae},
volume = {189},
year = {2006},
pages = {1-10},
zbl = {1090.05020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm190-0-1}
}
Nafaa Chbili. Skein algebras of the solid torus and symmetric spatial graphs. Fundamenta Mathematicae, Tome 189 (2006) pp. 1-10. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm190-0-1/