mycielski_graph

mycielski_graph(n)[source]

Generator for the n_th Mycielski Graph.

The Mycielski family of graphs is an infinite set of graphs. M1 is the singleton graph, M2 is two vertices with an edge, and, for i>2, Mi is the Mycielskian of Mi1.

More information can be found at http://mathworld.wolfram.com/MycielskiGraph.html

Parameters
nint

The desired Mycielski Graph.

Returns
Mgraph

The n_th Mycielski Graph

Notes

The first graph in the Mycielski sequence is the singleton graph. The Mycielskian of this graph is not the P2 graph, but rather the P2 graph with an extra, isolated vertex. The second Mycielski graph is the P2 graph, so the first two are hard coded. The remaining graphs are generated using the Mycielski operation.