Geodesic
Convex and Weakly Convex Domination in Prism Graphs
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 3, pp. 741-755

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For a given graph G = (V;E) and permutation π : V ↦ V the prism πG of G is defined as follows: V (πG) = V (G) ∪ V (G′), where G′ is a copy of G, and E(πG) = E(G) ∪ E(G′) ∪ Mπ, where Mπ = uv′ : u ∈ V (G); v = π (u) and v′ denotes the copy of v in G′. We study and compare the properties of convex and weakly convex dominating sets in prism graphs. In particular, we characterize prism γcon-fixers and -doublers. We also show that the differences γwcon(G) – γwcon(πG) and γwcon (πG) – 2γwcon (G) can be arbitrarily large, and that the convex domination number of πG cannot be bounded in terms of γcon (G).
Keywords: domination, prism graphs 
Rosicka, Monika. Convex and Weakly Convex Domination in Prism Graphs. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 3, pp. 741-755. http://geodesic.mathdoc.fr/item/DMGT_2019_39_3_a9/
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