Note: On the 2-rainbow domination in graphs

Authors:
Boštjan Brešar;Tadeja Kraner Šumenjak
Affiliations:
FEECS, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia;FA, University of Maribor, Vrbanska 30, 2000 Maribor, Slovenia
Venue:
Discrete Applied Mathematics
Year:
2007

Citing 1
Cited 8

Graph classes: a survey

Graph classes: a survey

2-rainbow domination of generalized Petersen graphs P(n,2)

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Note: 2-rainbow domination in generalized Petersen graphs P(n,3)

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Rainbow domination on trees

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Difference between 2-rainbow domination and Roman domination in graphs

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Rainbow domination and related problems on strongly chordal graphs

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Rainbow domination in the lexicographic product of graphs

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A tight upper bound for 2-rainbow domination in generalized Petersen graphs

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On rainbow domination numbers of graphs

Information Sciences: an International Journal

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Abstract

The concept of 2-rainbow domination of a graph G coincides with the ordinary domination of the prism G@?K"2. In this paper, we show that the problem of deciding if a graph has a 2-rainbow dominating function of a given weight is NP-complete even when restricted to bipartite graphs or chordal graphs. Exact values of 2-rainbow domination numbers of several classes of graphs are found, and it is shown that for the generalized Petersen graphs GP(n,k) this number is between @?4n/5@? and n with both bounds being sharp.