Algorithm Let us choose as a beginning
point any vertex x of L', and any oriented edge (x,y) incident to
it. After coming to vertex y, we choose the middle of the three remaining
edges and orient it so that its beginning point is y. Continuing to apply
that rule, we will close a first circuit. It is a shadow of one component
of L. After that, we choose another vertex (the same or different from
the first) incident to at least one edge not used before, and we start
from that edge. We continue to apply the same algorithm until all the edges
of the graph are exhausted.
After tracing all circuits
in L' we obtain the first and simplest KL invariant- the component number
c. On the other hand, from every 4-valent plane graph L' we can obtain
a link L, such that L' is a shadow of L, and the number of circuits c in
L obtained by the Component Algorithm is the number of components
The LinKnot function
fComponentNo (webMathematica fComponentNo)
calculates the number of components of any KL.
In the existing KL tables,
all KLs are strongly divided into separate classes, according to the number
of components. In our discussion, we will try to work with all of them
together far as it is possible, trying to find some order in the complete
set of KLs and make their classification.