Sheikholeslami, S., Nazari-Moghaddam, S. (2019). On trees with equal Roman domination and outer-independent Roman domination numbers. Communications in Combinatorics and Optimization, (), -. doi: 10.22049/cco.2019.26319.1095

Seyed Mahmoud Sheikholeslami; Sakineh Nazari-Moghaddam. "On trees with equal Roman domination and outer-independent Roman domination numbers". Communications in Combinatorics and Optimization, , , 2019, -. doi: 10.22049/cco.2019.26319.1095

Sheikholeslami, S., Nazari-Moghaddam, S. (2019). 'On trees with equal Roman domination and outer-independent Roman domination numbers', Communications in Combinatorics and Optimization, (), pp. -. doi: 10.22049/cco.2019.26319.1095

Sheikholeslami, S., Nazari-Moghaddam, S. On trees with equal Roman domination and outer-independent Roman domination numbers. Communications in Combinatorics and Optimization, 2019; (): -. doi: 10.22049/cco.2019.26319.1095

On trees with equal Roman domination and outer-independent Roman domination numbers

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 $gamma_{R}(T)=gamma_{oiR}(T)$.