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

A spatial Kₙ-graph is an embedding of a complete graph Kₙ with n vertices in a $3$-sphere S³. Knots in a spatial Kₙ-graph corresponding to cycles of Kₙ are called constituent knots. We consider the case $n=4$. The boundary of the orientable band surface constructed from a spatial K₄-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 K₄-graphs, their θ-subgraphs and cyclic subgraphs with the Jones polynomials of constituent knots and related links. Bibliography: 25 titles.