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Given a graph $G$, a dominating set is a set of vertices $D$ such that every vertex of $G$ is in $D$ or adjacent to a vertex in $D$.
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Is the domination number of a combinatorial design determined by the design parameters?
Well, interestingly enough, all the 80 Steiner triple systems on 15 points have minimum dominating sets of size 10 - there is more tradeoff between the points/blocks than I first recognised.
But if w …