@article {
author = {Gonzalez Yero, Ismael and Cabrera Martinez, Abel},
title = {A characterization of trees with equal Roman {2}-domination and Roman domination numbers},
journal = {Communications in Combinatorics and Optimization},
volume = {4},
number = {2},
pages = {95-107},
year = {2019},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2019.26364.1103},
abstract = {Given a graph $G=(V,E)$ and a vertex $v \in V$, by $N(v)$ we represent the open neighbourhood of $v$. Let $f:V\rightarrow \{0,1,2\}$ be a function on $G$. The weight of $f$ is $\omega(f)=\sum_{v\in V}f(v)$ and let $V_i=\{v\in V \colon f(v)=i\}$, for $i=0,1,2$. The function $f$ is said to be1) a Roman $\{2\}$-dominating function, if for every vertex $v\in V_0$, $\sum_{u\in N(v)}f(u)\geq 2$. The Roman $\{2\}$-domination number, denoted by $\gamma_{\{R2\}}(G)$, is the minimum weight among all Roman $\{2\}$-dominating functions on $G$;2) a Roman dominating function, if for every vertex $v\in V_0$ there exists $u\in N(v)\cap V_2$. The Roman domination number, denoted by $\gamma_R(G)$, is the minimum weight among all Roman dominating functions on $G$.It is known that for any graph $G$, $\gamma_{\{R2\}}(G)\leq \gamma_R(G)$. In this paper, we characterize the trees $T$ that satisfy the equality above.},
keywords = {Roman ${2}$-domination,$2$-rainbow domination,Roman domination,tree},
url = {http://comb-opt.azaruniv.ac.ir/article_13850.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13850_e789cd5a865ff841296b9739ea34aec1.pdf}
}