Simon Brezovnik (Author), Darja Rupnik Poklukar (Author), Janez Žerovnik (Author)

Abstract

A k-rainbow dominating function (kRDF) of G is a function that assigns subsets of {1, 2, ..., k} to the vertices of G such that for vertices v with f(v) = ∅ we have Uu∈N(v)f(u) = {1, 2, ..., k}. The weight w(f) of a kRDF f is defined as w(f) = P v∈V(G)|f(v)|. The minimum weight of a kRDF of G is called the k-rainbow domination number of G, which is denoted by γrk(G). In this paper, we study the 2-rainbow domination number of the Cartesian product of two cycles. Exact values are given for a number of infinite families and we prove lower and upper bounds for all other cases.

Keywords

2-rainbow domination;domination number;cartesian product;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FS - Faculty of Mechanical Engineering
UDC: 519.17
COBISS: 212017155 Link will open in a new window
ISSN: 1855-3966
Views: 12
Downloads: 0
Average score: 0 (0 votes)
Metadata: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Other data

Secondary language: Slovenian
Secondary keywords: 2-mavrična dominacija;dominacijsko število;kartezični produkt grafov;
Pages: 17 str.
Volume: ǂVol. ǂ25
Issue: ǂno. ǂ3
Chronology: 2025
DOI: 10.26493/1855-3974.3168.74d
ID: 26465189