mycielski_graph¶

mycielski_graph(n)[source]¶

Generator for the n_th Mycielski Graph.

The Mycielski family of graphs is an infinite set of graphs. $M_{1}$ is the singleton graph, $M_{2}$ is two vertices with an edge, and, for $i > 2$ , $M_{i}$ is the Mycielskian of $M_{i - 1}$ .

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 $P_{2}$ graph, but rather the $P_{2}$ graph with an extra, isolated vertex. The second Mycielski graph is the $P_{2}$ graph, so the first two are hard coded. The remaining graphs are generated using the Mycielski operation.