A dominating set of vertices S of a graph G is connected if the subgraph G[S] is connected. Let γc(G) denote the size of any smallest connected dominating set in G. A graph G is k-γ-connected-critical if γc(G)=k, but if any edge e∈E(G¯) is added to G, then γc(G+e)⩽k-1. This is a variation on the earlier concept of criticality of
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