Elsevier

Discrete Applied Mathematics

Volume 204, 11 May 2016, Pages 22-28
Discrete Applied Mathematics

Roman {2}-domination

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Abstract

In this paper, we initiate the study of a variant of Roman dominating functions. For a graph G=(V,E), a Roman {2}-dominating function f:V{0,1,2} has the property that for every vertex vV with f(v)=0, either v is adjacent to a vertex assigned 2 under f, or v is adjacent to least two vertices assigned 1 under f. The weight of a Roman {2}-dominating function is the sum vVf(v), and the minimum weight of a Roman {2}-dominating function f is the Roman {2}-domination number. First, we present bounds relating the Roman {2}-domination number to some other domination parameters. In particular, we show that the Roman {2}-domination number is bounded above by the 2-rainbow domination number. Moreover, we prove that equality between these two parameters holds for trees and cactus graphs with no even cycles. Finally, we show that associated decision problem for Roman {2}-domination is NP-complete, even for bipartite graphs.

Keywords

Roman domination
Roman {2}-domination
Weak Roman domination
2-rainbow domination
2-domination

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