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For a given graph $G=(V,E)$ and permutation $pi:Vmapsto V$ the prism $pi G$ of $G$ is defined as follows: $V(pi G)=V(G)cup V(Gu0027)$, where $Gu0027$ is a copy of $G$, and $E(pi G)=E(G)cup E(Gu0027)cup M_{pi}$, where $M_{pi}={uvu0027: uin V(G), v=pi(u)}$ and $vu0027$ denotes the copy of $v$ in $Gu0027$.  study and compare the properties of convex and weakly convex dominating sets in prism graphs. In particular, we characterize prism $gamma_{con}$-fixers and -doublers. We also show that the differences $gamma_{wcon}(G)-gamma_{wcon}(pi G)$ and $gamma_{wcon}(pi G) - 2gamma_{wcon}(G)$ can be arbitrarily large, and that the convex domination number of $pi G$ cannot be bounded in terms of $gamma_{con}(G).$

Convex and weakly convex domination in prism graphs