Issue |
RAIRO-Oper. Res.
Volume 56, Number 4, July-August 2022
|
|
---|---|---|
Page(s) | 2293 - 2304 | |
DOI | https://doi.org/10.1051/ro/2022089 | |
Published online | 29 July 2022 |
Restrained double Roman domination of a graph
1
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
2
Department of Mathematics, University of Tafresh, Tafresh, Iran
3
Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen, Germany
* Corresponding author: damojdeh@umz.ac.ir
Received:
13
June
2021
Accepted:
26
May
2022
For a graph G = (V, E), a restrained double Roman dominating function is a function f : V → {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 w with f(w) ≥ 2, and at the same time, the subgraph G[V0] which includes vertices with zero labels has no isolated vertex. The weight of a restrained double Roman dominating function f is the sum f(V) = ∑v∈V f(v), and the minimum weight of a restrained double Roman dominating function on G is the restrained double Roman domination number of G. We initiate the study of restrained double Roman domination with proving that the problem of computing this parameter is NP-hard. Then we present an upper bound on the restrained double Roman domination number of a connected graph G in terms of the order of G and characterize the graphs attaining this bound. We study the restrained double Roman domination versus the restrained Roman domination. Finally, we investigate the bounds for the restrained double Roman domination of trees and determine trees T attaining the exhibited bounds.
Key words: 05C69
Key words: Domination / restrained Roman domination / restrained double Roman domination
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
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