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A set S of vertices in a graph G is a dominating set of G if every vertex of V(G)∖S is adjacent to some vertex in S. The minimum cardinality of a dominating set of G is the domination number of G, denoted as γ(G). Let Pn and Cn denote a path and a cycle, respectively, on n vertices. Let k1(F) and k2(F) denote the number of components of a graph F that are isomorphic to a graph in the family {P3,P4,P5,C5}...
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