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The distance d G(u, v) between two vertices u and v in a connected graph G is the length of the shortest uv-path in G. A uv-path of length d G(u, v) is called a uv-geodesic. A set X is convex in G if vertices from all ab-geodesics belong to X for any two vertices a, bX. The convex domination number γcon(G) of a graph G equals the minimum cardinality of a convex dominating set. In the paper, Nordhaus-Gaddum-type results for the convex domination number are studied.

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