Geodesic
Graphs with convex domination number close to their order
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 2, pp. 307-316.

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For a connected graph G = (V,E), a set D ⊆ V(G) is a dominating set of G if every vertex in V(G)-D has at least one neighbour in D. The distance d_G(u,v) between two vertices u and v is the length of a shortest (u-v) path in G. An (u-v) path of length d_G(u,v) is called an (u-v)-geodesic. A set X ⊆ V(G) is convex in G if vertices from all (a-b)-geodesics belong to X for any two vertices a,b ∈ X. A set X is a convex dominating set if it is convex and dominating. The convex domination number γ_con(G) of a graph G is the minimum cardinality of a convex dominating set in G. Graphs with the convex domination number close to their order are studied. The convex domination number of a Cartesian product of graphs is also considered.
Keywords: convex domination, Cartesian product 
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Cyman, Joanna; Lemańska, Magdalena; Raczek, Joanna. Graphs with convex domination number close to their order. Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 2, pp. 307-316. http://geodesic.mathdoc.fr/item/DMGT_2006_26_2_a11/

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