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- W2092368006 abstract "A k-rainbow dominating function of a graph G is a map f from V(G) to the set of all subsets of {1,2,…,k} such that {1,…,k}=⋃u∈N(v)f(u) whenever v is a vertex with f(v)=0̸. The k-rainbow domination number of G is the invariant γrk(G), which is the minimum sum (over all the vertices of G) of the cardinalities of the subsets assigned by a k-rainbow dominating function. We focus on the 2-rainbow domination number of the lexicographic product of graphs and prove sharp lower and upper bounds for this number. In fact, we prove the exact value of γr2(G∘H) in terms of domination invariants of G except for the case when γr2(H)=3 and there exists a minimum 2-rainbow dominating function of H such that there is a vertex in H with the label {1,2}." @default.
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- W2092368006 date "2013-09-01" @default.
- W2092368006 modified "2023-10-04" @default.
- W2092368006 title "Rainbow domination in the lexicographic product of graphs" @default.
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- W2092368006 doi "https://doi.org/10.1016/j.dam.2013.03.011" @default.
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