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On stratification and domination in prisms. (English) Zbl 1237.05149
Summary: A graph $$G$$ is 2-stratified if its vertex set partitioned into two color classes. We color the vertices in one color class red and the other class blue. Let $$F$$ be a 2-stratified graph with one fixed blue vertex $$v$$ specified. We say that $$F$$ is rooted at $$v$$. The $$F$$-domination number of a graph $$G$$ is the minimum number of red vertices of $$G$$ in a redblue coloring of the vertices of $$G$$ such that every blue vertex $$v$$ of $$G$$ belongs to a copy of $$F$$ rooted at $$v$$. In this paper we investigate the $$F$$- domination number of prisms when $$F$$ is 2-stratified 6-cycle rooted at a blue vertex. And we get a new generalization result of stratified domination number for prisms.
##### MSC:
 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C15 Coloring of graphs and hypergraphs
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