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- W2201557213 abstract "For a graph $G = (V, E)$, a Roman dominating function $f : V rightarrow {0, 1, 2}$ has the property that every vertex $v in V $with $f (v) = 0$ has a neighbor $u$ with $f (u) = 2$. The weight of a Roman dominating function $f$ is the sum $f (V) = cup_{vin V} f (v)$, and the minimum weight of a Roman dominating function on $G$ is the Roman domination number $gamma_R(G)$ of $G$. The Roman bondage number $b_R(G)$ of $G$ is the minimum cardinality of all sets $F subseteq E$ for which $gamma_R(G - F) > gamma_R(G)$. A graph $G$ is in the class $mathcal{R}_{UVR}$ if the Roman domination number remains unchanged when a vertex is deleted. In this paper we obtain tight upper bounds for $gamma_R(G)$ and $b_R(G)$ provided a graph $G$ is in $mathcal{R}_{UVR}$. We present necessary and sufficient conditions for a tree to be in the class $mathcal{R}_{UV R}$. We give a constructive characterization of $mathcal{R}_{UVR}$-trees using labellings." @default.
- W2201557213 created "2016-06-24" @default.
- W2201557213 creator A5027008906 @default.
- W2201557213 date "2015-08-09" @default.
- W2201557213 modified "2023-09-27" @default.
- W2201557213 title "Roman domination in graphs: the class $mathcal{R}_mathbf{UV R}$" @default.
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- W2201557213 hasPublicationYear "2015" @default.
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