Polynomials of complete spatial graphs and Jones polynomials of the related links

A spatial $\mathbb K_n$-graph is an embedding of a complete graph $\mathbb K_n$ with $n$ vertices in a $3$-sphere $S^3$. Knots in a spatial $\mathbb K_n$-graph corresponding to cycles of $\mathbb K_n$ are called constituent knots. We consider the case $n=4$. The boundary of the orientable band surface constructed from a spatial $\mathbb K_4$-graph and having the zero Seifert form is a 4-component link, which is referred to as the associated link. We obtain formulae relating the normalized Yamada and Jaeger polynomials of spatial $\mathbb K_4$-graphs, their $\theta$-subgraphs and cyclic subgraphs with the Jones polynomials of constituent knots and related links. Bibliography: 25 titles.