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- W4287376053 abstract "Let $G=(V,E)$ be a graph. A subset $D$ of $V$ is a textit{restrained dominating set} if every vertex in $V setminus D$ is adjacent to a vertex in $D$ and to a vertex in $V setminus D$. The textit{restrained domination number}, denoted by $gamma_r(G)$, is the smallest cardinality of a restrained dominating set of $G$. A function $f : V rightarrow {0, 1, 2}$ is a textit{restrained Italian dominating function} on $G$ if (i) for each vertex $v in V$ for which $f(v)=0$, it holds that $sum_{u in N_G(v)} f(u) geq 2$, (ii) the subgraph induced by ${v in V mid f(v)=0 }$ has no isolated vertices. The textit{restrained Italian domination number}, denoted by $gamma_{rI}(G)$, is the minimum weight taken over all restrained Italian dominating functions of $G$. It is known that $gamma_r(G) leq gamma_{rI}(G) leq 2gamma_r(G)$ for any graph $G$. In this paper, we characterize the trees $T$ for which $gamma_r(T) = gamma_{rI}(T)$, and we also characterize the trees $T$ for which $gamma_{rI}(T) = 2gamma_r(T)$." @default.
- W4287376053 created "2022-07-25" @default.
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- W4287376053 date "2021-01-16" @default.
- W4287376053 modified "2023-10-16" @default.
- W4287376053 title "Restrained Italian domination in trees" @default.
- W4287376053 hasPublicationYear "2021" @default.
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