Delta link-homotopy on spatial graphs

Abstract

We study new equivalence relations in spatial graph theory. We consider natural generalizations of delta link-homotopy on links, which is an equivalence relation generated by delta moves on the same component and ambient isotopies. They are stronger than edge-homotopy and vertex-homotopy on spatial graphs which are natural generalizations of link-homotopy on links. Relationship to existing familiar equivalence relations on spatial graphs are stated, and several invariants are de_ned by using the second coeÆcient of the Conway polynomial and the third derivative at 1 of the Jones polynomial of a knot.