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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.
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C15 Coloring of graphs and hypergraphs
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