Rainbow domination in the lexicographic product of graphs
نویسندگان
چکیده
منابع مشابه
Rainbow domination in the lexicographic product of graphs
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) = ∅. 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 focu...
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Lexicographic product G◦H of two graphs G and H has vertex set V (G)×V (H) and two vertices (u1, v1) and (u2, v2) are adjacent whenever u1u2 ∈ E(G), or u1 = u2 and v1v2 ∈ E(H). If every matching of G of size k can be extended to a perfect matching in G, then G is called k-extendable. In this paper, we study matching extendability in lexicographic product of graphs. The main result is that the l...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.03.011