ǂThe ǂ2-rainbow domination number of Cartesian product of cycles

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

Povzetek

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.

Ključne besede

2-rainbow domination;domination number;cartesian product;

Podatki

Jezik:	Angleški jezik
Leto izida:	2025
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FS - Fakulteta za strojništvo
UDK:	519.17
COBISS:	212017155
ISSN:	1855-3966
Št. ogledov:	12
Št. prenosov:	0
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Slovenski jezik
Sekundarne ključne besede:	2-mavrična dominacija;dominacijsko število;kartezični produkt grafov;
Strani:	17 str.
Letnik:	ǂVol. ǂ25
Zvezek:	ǂno. ǂ3
Čas izdaje:	2025
DOI:	10.26493/1855-3974.3168.74d
ID:	26465189