期刊论文详细信息
Communications in Combinatorics and Optimization | |
An upper bound on triple Roman domination | |
article | |
M. Hajjari1  Hossein Abdollahzadeh Ahangar2  Rana Khoeilar1  Zehui Shao3  S.M. Sheikholeslami1  | |
[1]Azarbaijan Shahid Madani University | |
[2]Babol Noshirvani University of Technology | |
[3]Guangzhou University | |
关键词: Triple Roman dominating function; Triple Roman domination number; Trees; | |
DOI : 10.22049/cco.2022.27816.1359 | |
学科分类:社会科学、人文和艺术(综合) | |
来源: Azarbaijan Shahide Madani Universit | |
【 摘 要 】
For a graph $G=(V,E)$, a triple Roman dominating function (3RD-function) is a function $f:V\to \{0,1,2,3,4\}$ having the property that (i) if $f(v)=0$ then $v$ must have either one neighbor $u$ with $f(u)=4$, or two neighbors $u,w$ with $f(u)+f(w)\ge 5$ or three neighbors $u,w,z$ with $f(u)=f(w)=f(z)=2$, (ii) if $f(v)=1$ then $v$ must have one neighbor $u$ with $f(u)\ge 3$ or two neighbors $u,w$ with $f(u)=f(w)=2$, and (iii) if $f(v)=2$ then $v$ must have one neighbor $u$ with $f(u)\ge 2$. The weight of a 3RDF $f$ is the sum $f(V)=\sum_{v\in V} f(v)$, and the minimum weight of a 3RD-function on $G$ is the triple Roman domination number of $G$, denoted by $\gamma_{[3R]}(G)$. In this paper, we prove that for any connected graph $G$ of order $n$ with minimum degree at least two, $\gamma_{[3R]}(G)\leq \frac{3n}{2}$.【 授权许可】
CC BY-SA
【 预 览 】
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