Independent 2-rainbow domination in trees

Author:

Amjadi J.1,Dehgardi N.1,Mohammadi N.1,Sheikholeslami S. M.1,Volkmann L.2

Affiliation:

1. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

2. Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen, Germany

Abstract

A 2-rainbow dominating function (2RDF) on a graph G is a function f from the vertex set V(G) to the set of all subsets of the set {1, 2} such that for any vertex v ∈ V(G) with f(v) = ∅ the condition ⋃u∈N(v)f(u) = {1, 2} is fulfilled. A 2RDF f is independent 2-rainbow dominating function (I2RDF) if no two vertices assigned nonempty sets are adjacent. The weight of a 2RDF f is the value ω(f) = ∑v∈V |f(v)|. The 2-rainbow domination number γr2(G) (respectively, the independent 2-rainbow domination number ir2(G)) is the minimum weight of a 2RDF (respectively, I2RDF) on G. M. Chellali and N. Jafari Rad [Independent 2-rainbow domination in graphs, to appear in J. Combin. Math. Combin. Comput.] have studied the independent 2-rainbow domination numbers in graphs and posed the following problem: Find a sharp bound for ir2(T) in terms of the order of a tree T. In this paper we prove that for every tree T of order n ≥ 3, [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Independent k-rainbow bondage number of graphs;AKCE International Journal of Graphs and Combinatorics;2023-08-24

2. A new upper bound on the independent 2-rainbow domination number in trees;COMMUN COMB OPTIM;2022

3. (Independent) $k$-Rainbow Domination of a Graph;Turkish Journal of Mathematics and Computer Science;2020-12-31

4. Rainbow Domination in Graphs;Topics in Domination in Graphs;2020

5. General upper bounds on independentk-rainbow domination;Discrete Applied Mathematics;2019-04

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