Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

# networkx.algorithms.dominating.dominating_set¶

dominating_set(G, start_with=None)[source]

Finds a dominating set for the graph G.

A dominating set for a graph with node set V is a subset D of V such that every node not in D is adjacent to at least one member of D 1.

Parameters
• G (NetworkX graph)

• start_with (node (default=None)) – Node to use as a starting point for the algorithm.

Returns

D – A dominating set for G.

Return type

set

Notes

This function is an implementation of algorithm 7 in 2 which finds some dominating set, not necessarily the smallest one.

References

1

https://en.wikipedia.org/wiki/Dominating_set

2

Abdol-Hossein Esfahanian. Connectivity Algorithms. http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf