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      Roman Bondage Numbers of Some Graphs

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          Abstract

          A Roman dominating function on a graph G=(V,E) is a function f:V{0,1,2} satisfying the condition that every vertex u with f(u)=0 is adjacent to at least one vertex v with f(v)=2. The weight of a Roman dominating function is the value f(G)=uVf(u). The Roman domination number of G is the minimum weight of a Roman dominating function on G. The Roman bondage number of a nonempty graph G is the minimum number of edges whose removal results in a graph with the Roman domination number larger than that of G. This paper determines the exact value of the Roman bondage numbers of two classes of graphs, complete t-partite graphs and (n3)-regular graphs with order n for any n5.

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          Roman domination in graphs

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            The bondage number of a graph

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              Extremal Problems for Roman Domination

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                Author and article information

                Journal
                18 September 2011
                Article
                1109.3933
                5b569e4c-c0df-4412-9a2d-889a5db8819a

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                05C69
                10 pages
                math.CO

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