@article {
author = {Volkmann, Lutz},
title = {Double Roman domination and domatic numbers of graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {3},
number = {1},
pages = {71-77},
year = {2018},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2018.26125.1078},
abstract = {A double Roman dominating function on a graph $G$ with vertex set $V(G)$ is defined in cite{bhh} as a function $f:V(G)\to \{0,1,2,3\}$ having the property that if $f(v)=0$, then the vertex $v$ must have at least two neighbors assigned 2 under $f$ or one neighbor $w$ with $f(w)=3$, and if $f(v)=1$, then the vertex $v$ must have at least one neighbor $u$ with $f(u)\ge 2$. The weight of a double Roman dominating function $f$ is the sum $\sum_{v\in V(G)}f(v)$, and the minimum weight of a double Roman dominating function on $G$ is the double Roman domination number $\gamma_{dR}(G)$ of $G$.A set $\{f_1,f_2, \dots,f_d\}$ of distinct double Roman dominating functions on $G$ with the property that $\sum_{i=1}^df_i(v)\le 3$ for each $v\in V(G)$ is called a double Roman dominating family (of functions) on $G$. The maximum number of functions in a double Roman dominating family on $G$ is the double Roman domatic number of $G$.In this note we continue the study the double Roman domination and domatic numbers. In particular, we present a sharp lower bound on $\gamma_{dR}(G)$, and we determine the double Roman domination and domatic numbers of some classes of graphs.},
keywords = {domination,Double Roman domination number,Double Roman domatic number},
url = {http://comb-opt.azaruniv.ac.ir/article_13744.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13744_0b21f0f7d95e9ab99c3422cf6f3acc77.pdf}
}