On Cartesian Products Having a Minimum Dominating Set that is a Box or a Stairway
نویسندگان
چکیده
In this note we characterize the pairs of graphs G and H, for which γ(G H) equals min{|V (G)|, |V (H)|}. Notably, assuming that |V (G)| ≤ |V (H)|, G can be an arbitrary graph, and H is a join L ⊕ F , where L is any spanning supergraph of the graph L(G : A1, . . . , A`), which is determined by a partition (A1, . . . , A`) of V (G) and F is any graph such that |V (F )| ≥ |V (G)| − `. Furthermore we give some sufficient and some necessary conditions for pairs of graphs G and H to satisfy γ(G H) = min{γ(G)|V (H)|, |V (G)|γ(H)}.
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عنوان ژورنال:
- Graphs and Combinatorics
دوره 31 شماره
صفحات -
تاریخ انتشار 2015