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On trees with equal Roman domination and outer-independent Roman domination numbers | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 10، دوره 4، شماره 2، اسفند 2019، صفحه 185-199 اصل مقاله (400.74 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2019.26319.1095 | ||
| نویسندگان | ||
| S. Nazari-Moghaddam؛ S.M. Sheikholeslami* | ||
| Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran | ||
| چکیده | ||
| A Roman dominating function (RDF) on a graph $G$ is a function $f : V (G) \to \{0, 1, 2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) = 2$. A Roman dominating function $f$ is called an outer-independent Roman dominating function (OIRDF) on $G$ if the set $\{v\in V\mid f(v)=0\}$ is independent. The (outer-independent) Roman domination number $\gamma_{R}(G)$ ($\gamma_{oiR}(G)$) is the minimum weight of an RDF (OIRDF) on $G$. Clearly for any graph $G$, $\gamma_{R}(G)\le \gamma_{oiR}(G)$. In this paper, we provide a constructive characterization of trees $T$ with $\gamma_{R}(T)=\gamma_{oiR}(T)$. | ||
| کلیدواژه‌ها | ||
| Roman domination؛ outer-independent Roman domination؛ tree | ||
| مراجع | ||
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