# Parameter: minimum dominating set

Definition:

A dominating set of a graph $G$ is a subset $D$ of its vertices, such that every vertex not in $D$ is adjacent to at least one member of $D$. The parameter minimum dominating set for graph $G$ is the minimum number of vertices in a dominating set for $G$.

## Relations

Minimal/maximal is with respect to the contents of ISGCI. Only references for direct bounds are given. Where no reference is given, check equivalent parameters.

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## Problems

Problems in italics have no summary page and are only listed when ISGCI contains a result for the current parameter.

3-Colourability Unknown to ISGCI [+]Details
Clique Unknown to ISGCI [+]Details
Clique cover Unknown to ISGCI [+]Details
Colourability Unknown to ISGCI [+]Details
Domination Unknown to ISGCI [+]Details
Feedback vertex set Unknown to ISGCI [+]Details
Graph isomorphism Unknown to ISGCI [+]Details
Hamiltonian cycle Unknown to ISGCI [+]Details
Hamiltonian path Unknown to ISGCI [+]Details
Independent set Unknown to ISGCI [+]Details
Maximum cut Unknown to ISGCI [+]Details
Monopolarity Unknown to ISGCI [+]Details
Polarity Unknown to ISGCI [+]Details
Weighted clique Unknown to ISGCI [+]Details
Weighted feedback vertex set Unknown to ISGCI [+]Details
Weighted independent set Unknown to ISGCI [+]Details