Every embedding can be described by an embedding adjacency matrix. In every part of it, the first vertex is followed by a sequence of its adjacent vertices given in the same (left or right) cyclic order. For the ending points, only the cyclic permutation corresponding to them is important, and not their particular position in the permutation. For example, a planar embedding of the octahedron graph
is
The LinKnot function
fPlanarEmbGraph (webMathematica fPlanarEmbGraph) gives the planar embedding of a 3connected planar graph
given by a list of unordered pairs. The output is a list that consists
of the input graph, its planar embedding, and the faces of the planar embedded
graph. The basis of this program is the external program planarity.exe
written by J.M. Boyer (Boyer and Myrvold, 2004). The LinKnot function
DrawPlanarEmbGraph (webMathematica DrawPlanarEmbGraph) draws a planar embedding of a graph given by a list
of unordered pairs, and the function Draw PlanarEmbKL draws a planar embedding
of a KL without showing double edges. The basis of those functions is the
program 3Dimensional Convex Drawings of 3Connected Planar Graphs
by M.Ochiai, N.Imafuji and N.Morimura.
