A note on the double Roman domination number of graphs

Chen, Xue-Gang. "A note on the double Roman domination number of graphs." Czechoslovak Mathematical Journal 70.1 (2020): 205-212. <http://eudml.org/doc/297225>.

@article{Chen2020,
abstract = {For a graph $G=(V,E)$, a double Roman dominating function is a function $f\colon V\rightarrow \lbrace 0,1,2,3\rbrace $ 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 with $f(w)=3$, and if $f(v)=1$, then the vertex $v$ must have at least one neighbor with $f(w)\ge 2$. The weight of a double Roman dominating function $f$ is the sum $f(V)=\sum \nolimits _\{v\in V\}f(v)$. The minimum weight of a double Roman dominating function on $G$ is called the double Roman domination number of $G$ and is denoted by $\gamma _\{\rm dR\}(G)$. In this paper, we establish a new upper bound on the double Roman domination number of graphs. We prove that every connected graph $G$ with minimum degree at least two and $G\ne C_\{5\}$ satisfies the inequality $\gamma _\{\rm dR\}(G)\le \lfloor \frac\{13\}\{11\}n\rfloor $. One open question posed by R. A. Beeler et al. has been settled.},
author = {Chen, Xue-Gang},
journal = {Czechoslovak Mathematical Journal},
keywords = {double Roman domination number; domination number; minimum degree},
language = {eng},
number = {1},
pages = {205-212},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on the double Roman domination number of graphs},
url = {http://eudml.org/doc/297225},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Chen, Xue-Gang
TI - A note on the double Roman domination number of graphs
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 1
SP - 205
EP - 212
AB - For a graph $G=(V,E)$, a double Roman dominating function is a function $f\colon V\rightarrow \lbrace 0,1,2,3\rbrace $ 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 with $f(w)=3$, and if $f(v)=1$, then the vertex $v$ must have at least one neighbor with $f(w)\ge 2$. The weight of a double Roman dominating function $f$ is the sum $f(V)=\sum \nolimits _{v\in V}f(v)$. The minimum weight of a double Roman dominating function on $G$ is called the double Roman domination number of $G$ and is denoted by $\gamma _{\rm dR}(G)$. In this paper, we establish a new upper bound on the double Roman domination number of graphs. We prove that every connected graph $G$ with minimum degree at least two and $G\ne C_{5}$ satisfies the inequality $\gamma _{\rm dR}(G)\le \lfloor \frac{13}{11}n\rfloor $. One open question posed by R. A. Beeler et al. has been settled.
LA - eng
KW - double Roman domination number; domination number; minimum degree
UR - http://eudml.org/doc/297225
ER -