 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.