Nordhaus-Gaddum results for the convex domination number of a graph

The distance dG(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 dG(u, v) is called uv-geodesic. A set X is convex in G if vertices from all ab-geodesics belong to X for every two vertices a, b ∈ X. The convex domination number γcon(G) of a graph G equals the minimum cardinality of a convex dominating set. There are a large number of results in the graph theory literature of the form α+ ᾱ ≤ n± for a domination parameter α. This kind of results is called Nordhaus-Gaddum-type results. The classical paper of Nordhaus and Gaddum [1] established this kind of inequalities for the chromatic numbers Here Nordhaus-Gaddum-type results for the convex domination number are studied.