On the outer independent 2-rainbow domination number of Cartesian products of paths and cycles

Communications in Combinatorics and Optimization

article

Dehgardi, Nasrin¹ 

[1] Sirjan University of Technology

关键词: 2-rainbow dominating function;    2-rainbow domination number;    outer independent 2-rainbow dominating function;    outer independent 2-rainbow dominationnumber;    Cartesian product;   

DOI  :  10.22049/cco.2021.27067.1188

学科分类：社会科学、人文和艺术（综合）

来源: Azarbaijan Shahide Madani Universit

【 摘 要 】

Let G be a graph. A 2-rainbow dominating function (or 2-RDF) of Gis a function f from V (G) to the set of all subsets of the set {1, 2} such that for avertex v ∈ V (G) with f(v) = ∅, the condition Su∈NG(v)f(u) = {1, 2} is fulfilled,where NG(v) is the open neighborhood of v. The weight of 2-RDF f of G is the valueω(f) := Pv∈V (G)|f(v)|. The 2-rainbow domination number of G, denoted by γr2(G),is the minimum weight of a 2-RDF of G. A 2-RDF f is called an outer independent2-rainbow dominating function (or OI2-RDF) of G if the set of all v ∈ V (G) withf(v) = ∅ is an independent set. The outer independent 2-rainbow domination numberγoir2(G) is the minimum weight of an OI2-RDF of G. In this paper, we obtain theouter independent 2-rainbow domination number of PmPn and PmCn. Also wedetermine the value of γoir2(Cm✷Cn) when m or n is even.

【 授权许可】

CC BY-SA