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- W2947573181 abstract "Let $G=(V,E)$ be a graph. A subset $Ssubset V$ is a hop dominating setif every vertex outside $S$ is at distance two from a vertex of$S$. A hop dominating set $S$ which induces a connected subgraph is called a connected hop dominating set of $G$. Theconnected hop domination number of $G$, $ gamma_{ch}(G)$, is the minimum cardinality of a connected hopdominating set of $G$. A hopRoman dominating function (HRDF) of a graph $G$ is a function $f: V(G)longrightarrow {0, 1, 2} $ having the property thatfor every vertex $ v in V $ with $ f(v) = 0 $ there is avertex $ u $ with $ f(u)=2 $ and $ d(u,v)=2 $.The weight ofan HRDF $ f $ is the sum $f(V) = sum_{vin V} f(v) $. Theminimum weight of an HRDF on $ G $ is called the hop Romandomination number of $ G $ and is denoted by $ gamma_{hR}(G)$. We give an algorithmthat decides whether $gamma_{hR}(T)=2gamma_{ch}(T)$ for a giventree $T$." @default.
- W2947573181 created "2019-06-07" @default.
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- W2947573181 date "2019-12-01" @default.
- W2947573181 modified "2023-09-24" @default.
- W2947573181 title "On Hop Roman Domination in Trees" @default.
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- W2947573181 doi "https://doi.org/10.22049/cco.2019.26469.1116" @default.
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