= Independent dominating set
An <independent dominating set> is simultaneously an <independent set> and a <dominating set>. Equivalently, it is an <independent set> maximal under inclusion: an outside <vertex> can be added while preserving independence exactly when it has no neighbour in the selected <set>. On a <triangle in a graph>, any singleton is an <independent dominating set> but no <independent vertex cover> exists. Independence and domination are directly expressible in <first-order logic> when a fixed bound on the number of selected <vertices> is given.
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