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A subset S of vertices in a graph G=(V,E) is a connected dominating set of G if every vertex of V∖S is adjacent to a vertex in S and the subgraph induced by S is connected. The minimum cardinality of a connected dominating set of G is the connected domination number γc(G). The girth g(G) is the length of a shortest cycle in G. We show that if G is a connected graph that contains at least one cycle,...
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