@article {
author = {Dehgardi, Nasrin and Chellali, M},
title = {Outer independent Roman domination number of trees},
journal = {Communications in Combinatorics and Optimization},
volume = {6},
number = {2},
pages = {273-286},
year = {2021},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2021.27072.1191},
abstract = {A Roman dominating function (RDF) on a graph $G=(V,E)$ is a function $f:V\rightarrow \{0,1,2\}$ such that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. An RDF $f$ is called an outer independent Roman dominating function (OIRDF) if the set of vertices assigned a $0$ under $f$ is an independent set. The weight of an OIRDF is the sum of its function values over all vertices, and the outer independent Roman domination number $\gamma _{oiR}(G)$ is the minimum weight of an OIRDF on $G$. In this paper, we show that if $T$ is a tree of order $n\geq 3$ with $s(T)$ support vertices, then $\gamma _{oiR}(T)\leq \min \{\frac{5n}{6},\frac{3n+s(T)}{4}\}.$ Moreover, we characterize the tress attaining each bound.},
keywords = {Outer independent Roman dominating function,outer independent Roman domination number,tree},
url = {http://comb-opt.azaruniv.ac.ir/article_14162.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14162_bc649d348f3b3863bd5517b8d106538d.pdf}
}