@article {
author = {Sheikholeslami, Seyed Mahmoud and Nazari-Moghaddam, Sakineh},
title = {On trees with equal Roman domination and outer-independent Roman domination numbers},
journal = {Communications in Combinatorics and Optimization},
volume = {4},
number = {2},
pages = {185-199},
year = {2019},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2019.26319.1095},
abstract = {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 $\gamma_{R}(T)=\gamma_{oiR}(T)$. },
keywords = {Roman domination,outer-independent Roman domination,tree},
url = {http://comb-opt.azaruniv.ac.ir/article_13865.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13865_778d0f97a1447e3fa6dcc653002a9d16.pdf}
}