Graphics Reference
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areneeded for even N
.Itis funtosee why.Label
the N vertices of a graph with the indices of the variables X
i
, i
=
M,andM
+
foroddN
=
M
+
=
,...,N,asshown
inFig.
.
for N
.Anedgejoining vertex i with j signifies that theaxes indexed by
i,jare adjacent. hegraph on the let is a Hamilton path,becauseitcontainsallofthe
vertices. Such paths have been studied since Euler first did so in the eighteenth cen-
tury, and have modern applications to the “travelling salesman” problem and others
=
Figure
.
.
(Let) Parallel coordinates induce a point ℓ
ℓline duality. (Right) he horizontal position
of the point ℓ representing the line ℓ is determined only by the slope of the line m. he vertical line
ℓ
a
is represented by the point ℓ at the value a
on the X
axis
x
=
Figure
.
.
(Let) First Hamiltonian path on the vertices labeled
, ...,
corresponding to (axis) index
permutation
.(Right) he complete graph as the union of the three distinct Hamiltonian paths
starting successively at the vertices
,
,
