Abstract:
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.
Keywords:graph, knot, spatial graph, Jones polynomial, Yamada polynomial, Jaeger polynomial.
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