Convex and weakly convex domination in prism graphs

2017/12/20 by Rosicka, Monika
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.07545

Abstract

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')∪ M_π, where M_π=\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 γ_con-fixers and -doublers. We also show that the differences γ_wcon(G)-γ_wcon(πG) and γ_wcon(πG) - 2γ_wcon(G) can be arbitrarily large, and that the convex domination number of πG cannot be bounded in terms of γ_con(G).

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