Issue |
RAIRO-Oper. Res.
Volume 53, Number 2, April-June 2019
|
|
---|---|---|
Page(s) | 389 - 400 | |
DOI | https://doi.org/10.1051/ro/2018116 | |
Published online | 06 March 2019 |
Trees with equal Roman {2}-domination number and independent Roman {2}-domination number
1 Institute of Computing Science and Technology, Guangzhou University, 510006 Guangzhou, PR China .
2 School of Information Science and Engineering, Lanzhou University, 730000 Lanzhou, PR China .
3 School of Information Science and Technology, Chengdu University 610106 Chengdu, China .
4 Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran .
* Corresponding author: zshao@gzhu.edu.cn
Received:
11
June
2018
Accepted:
2
December
2018
A Roman {2}-dominating function (R{2}DF) on a graph G =(V, E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to either at least one vertex v with f(v) = 2 or two vertices v1, v2 with f(v1) = f(v2) = 1. The weight of an R{2}DF f is the value w(f) = ∑u∈Vf(u). The minimum weight of an R{2}DF on a graph G is called the Roman {2}-domination number γ{R2}(G) of G. An R{2}DF f is called an independent Roman {2}-dominating function (IR{2}DF) if the set of vertices with positive weight under f is independent. The minimum weight of an IR{2}DF on a graph G is called the independent Roman {2}-domination number i{R2}(G) of G. In this paper, we answer two questions posed by Rahmouni and Chellali.
Mathematics Subject Classification: 05C69
Key words: Roman {2}-domination / independent Roman {2}-domination / tree / algorithm
© EDP Sciences, ROADEF, SMAI 2019
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