grinpy.invariants.domination.min_dominating_set¶
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grinpy.invariants.domination.min_dominating_set(G)¶ Return a smallest dominating set in the graph.
The method to compute the set is brute force except that the subsets searched begin with those whose cardinality is equal to the sub-domination number of the graph, which was defined by Amos et al. and shown to be a tractable lower bound for the k-domination number.
- G : graph
- A Networkx graph.
- k : int
- A positive integer.
- minDominatingSet : list
- A smallest dominating set in the graph.
min_k_dominating_set
D. Amos, J. Asplund, B. Brimkov and R. Davila, The sub-k-domination number of a graph with applications to k-domination, arXiv preprint arXiv:1611.02379, (2016)