# networkx.generators.mycielski.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 $$M_{i-1}$$.

Parameters

n (int) – The desired Mycielski Graph.

Returns

M – The n_th Mycielski Graph

Return type

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.