Let $G=(V,E)$ be a graph. A subset $Ssubset V$ is a hop dominating set if 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 $G$. The connected hop domination number of $G$, $ gamma_{ch}(G)$, is the minimum cardinality of a connected hop dominating set of $G$. A hop Roman dominating function (HRDF) of a graph $G$ is a function $ f: V(G)longrightarrow {0, 1, 2} $ having the property that for every vertex $ v in V $ with $ f(v) = 0 $ there is a vertex $ u $ with $ f(u)=2 $ and $ d(u,v)=2 $. The weight of an HRDF $ f $ is the sum $f(V) = sum_{vin V} f(v) $. The minimum weight of an HRDF on $ G $ is called the hop Roman domination number of $ G $ and is denoted by $ gamma_{hR}(G) $. We give an algorithm that decides whether $gamma_{hR}(T)=2gamma_{ch}(T)$ for a given tree $T$.\ {bf Keywords:} hop dominating set, connected hop dominating set, hop Roman dominating function.
Jafari Rad, N., Poureidi, A. (2019). On Hop Roman Domination in Trees. Communications in Combinatorics and Optimization, 4(2), 201-208. doi: 10.22049/cco.2019.26469.1116
MLA
Nader Jafari Rad; Abolfazl Poureidi. "On Hop Roman Domination in Trees". Communications in Combinatorics and Optimization, 4, 2, 2019, 201-208. doi: 10.22049/cco.2019.26469.1116
HARVARD
Jafari Rad, N., Poureidi, A. (2019). 'On Hop Roman Domination in Trees', Communications in Combinatorics and Optimization, 4(2), pp. 201-208. doi: 10.22049/cco.2019.26469.1116
VANCOUVER
Jafari Rad, N., Poureidi, A. On Hop Roman Domination in Trees. Communications in Combinatorics and Optimization, 2019; 4(2): 201-208. doi: 10.22049/cco.2019.26469.1116
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