Generate a Petersen like graph.
This generates a graph which consists of two equal cardinality node sets. The subgraph induced by the set
|perimeter ||The length of the exterior cycle |
|skew ||Some value in the interval (0, .., perimeter) |
|_CT ||The controller object to manage the created graph|
0, 1, .., perimeter-1 of exterior nodes forms a cycle. Exterior and interior nodes are joined by the edges
(i, perimeter+i) with i in the interval
[0, .., perimeter). Interior nodes are joined by the edges
In the regular setting, perimeter and skew are relatively prime, and the subgraph induced by the second node set
perimeter, perimeter+1, .., 2*perimeter-1 also forms a cycle, but the node order is determined by the skew parameter. In any case, the generated graph is 3-node regular.
Up to the implicit arc orientations of the interior cycle,
skew = k and
skew = perimeter-k give the same graph. For
skew == 1, the result is a prism. For
skew == 2 and even perimeter, the result is planar.
The original Petersen graph is given by
generalizedPetersen(5,2). Some other graphs in this family have received special attention:
generalizedPetersen(6,2) is known as the Duerer graph,
generalizedPetersen(8,3) is known as the Moebius-Cantor graph,
generalizedPetersen(10,2) is the dodecahedron,
generalizedPetersen(10,3) is known as the Desargues graph.