# Convex and Weakly Convex Domination in Prism Graphs

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## Abstract

For a given graph G = (V;E) and permutation π : VV the prism πG of G is defined as follows: VG) = V (G) ∪ V (G′), where G′ is a copy of G, and E(πG) = E(G) ∪ E(G′) ∪M π, where M π = {uv′ : uV (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).

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# Discussiones Mathematicae Graph Theory

## The Journal of University of Zielona Góra

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Target Group

researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs

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