Prog. Theor. Phys. Supplement No.191 (2011) pp. 225-234
On Transforming a Spatial Graph into a Plane Graph
Department of Mathematics, Osaka City University, Osaka 558-8585, Japan
(Received September 15, 2010)
This article is a revised detailed version of the research
announcement [Bussei Kenkyu 92 (2009), 16]
introducing a complexity of a spatial graph, which is useful to
transform a spatial graph (without degree one vertices) into a plane
graph. We also introduce related topological invariants for every
spatial graph, called the warping degree, and
γ- warping degree and (γ,Γ)- warping degree.
We also generalize the usual unknotting number of a knot to every
spatial graph and introduce related topological
invariants for every spatial graph,
called the γ- unknotting number, Γ- unknotting number
and (γ,Γ)- unknotting number.
These invariants are used to define “semi-topological” invariants
for a spatial graph with degree one vertices, meaningful even for
a knotted arc.
DOI : 10.1143/PTPS.191.225
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