Polynomials of complete spatial graphs and Jones polynomial of related links

Let K_n be a complete graph with n vertices. An embedding of K_n in S^3 is called a spatial K_n-graph. Knots in a spatial K_n-graph corresponding to simple cycles of K_n are said to be constituent knots. We consider the case n=4. The boundary of an oriented band surface with zero Seifert form, constructed for a spatial K_4, is a four-component associated link. There are obtained relations between normalized Yamada and Jaeger polynomials of spatial graphs and Jones polynomials of constituent knots and the associated link.