A connected dominating set in a connected graph G is a dominating set in G whose vertices induce a connected subgraph, i.e., one in which there is no dominating vertex not connected to some other dominating vertex by an edge. Connected dominating sets therefore comprise a subset of all dominating sets in a graph. A minimum connected dominating set of a graph G is a connected dominating set of smallest possible size, where the minimum size is denoted d(G) and known as the connected domination number.
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