%0 Journal Article
%T On trees with equal Roman domination and outer-independent Roman domination numbers
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Sheikholeslami, Seyed Mahmoud
%A Nazari-Moghaddam, Sakineh
%D 2019
%\ 12/01/2019
%V 4
%N 2
%P 185-199
%! On trees with equal Roman domination and outer-independent Roman domination numbers
%K Roman domination
%K outer-independent Roman domination
%K tree
%R 10.22049/cco.2019.26319.1095
%X 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 ${vin Vmid f(v)=0}$ 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 $gamma_{R}(T)=gamma_{oiR}(T)$.
%U http://comb-opt.azaruniv.ac.ir/article_13865_778d0f97a1447e3fa6dcc653002a9d16.pdf