The 3-Rainbow Domination Number of the Cartesian Product of Cycles

Hong Gao, Changqing Xi and Yuansheng Yang
Additional contact information
Hong Gao: College of Science, Dalian Maritime University, Dalian 116026, China
Changqing Xi: College of Science, Dalian Maritime University, Dalian 116026, China
Yuansheng Yang: School of Computer Science and Technology, Dalian University of Technology, Dalian 116024, China

Mathematics, 2020, vol. 8, issue 1, 1-20

Abstract: We have studied the k -rainbow domination number of C n ? C m for k ≥ 4 (Gao et al. 2019), in which we present the 3-rainbow domination number of C n ? C m , which should be bounded above by the four-rainbow domination number of C n ? C m . Therefore, we give a rough bound on the 3-rainbow domination number of C n ? C m . In this paper, we focus on the 3-rainbow domination number of the Cartesian product of cycles, C n ? C m . A 3-rainbow dominating function (3RDF) f on a given graph G is a mapping from the vertex set to the power set of three colors { 1 , 2 , 3 } in such a way that every vertex that is assigned to the empty set has all three colors in its neighborhood. The weight of a 3RDF on G is the value ω ( f ) = ∑ v ∈ V ( G ) | f ( v ) | . The 3-rainbow domination number, γ r 3 ( G ) , is the minimum weight among all weights of 3RDFs on G . In this paper, we determine exact values of the 3-rainbow domination number of C 3 ? C m and C 4 ? C m and present a tighter bound on the 3-rainbow domination number of C n ? C m for n ≥ 5 .

Keywords: rainbow domination; graph domination; Cartesian product graph; cycle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/1/65/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/1/65/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:1:p:65-:d:304487

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().