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On Hop Roman Domination in Trees | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 10، دوره 4، شماره 2، زمستان 2019، صفحه 201-208 اصل مقاله (436.42 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2019.26469.1116 | ||
| نویسندگان | ||
Nader Jafari Rad  1؛ Abolfazl Poureidi2
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| 1Separtment of Mathemtics, Shahed University, Tehran, Iran | ||
| 2Department of Mathematics, Shahrood University of Technology, Shahrood, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| hop dominating set؛ connected hop dominating set؛ hop Roman dominating function | ||
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