We will discuss spatial embeddings of graphs into the 3-sphere. Since any cycle of a graph is embedding as a knot in the 3-sphere, the theory of spatial graphs can be considered as a generalization of the knot theory. Two spatial graphs are said to be equivalent if there is an ambient isotopy of the 3-sphere which transforms one spatial graph to another. As well as knots and links, spatial graphs can be studied from their diagrams. The Yamada polynomial is known as the most useful invariant of spatial graphs. Let K4 be the complete graph on 4 vertices. We will present a relation between normalized Yamada polynomials of a spatial K4-graph and its spatial subgraphs with Jones polynomial of the associated links.

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