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A set of vertices of a graph G such that each vertex of G is either in the set or is adjacent to a vertex in the set is called a dominating set of G. If additionally, the set of vertices induces a connected subgraph of G then the set is a connected dominating set of G. The domination number (G) of G is the smallest number of vertices in a dominating set of G, and the connected domination number c (G) of G is the smallest number of vertices in a connected dominating set of G. We find the connected domination numbers for all triangulations of up to thirteen vertices. For n 15, n 0 (mod 3), we find graphs of order n and c=n3. We also show that the difference c (G) - (G) can be arbitrarily large.
Bryant et al. (Fri,) studied this question.