On the double Roman domination in generalized petersen graphs P(5k,k)

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

Abstract

A double Roman dominating function on a graph G = (V, E) is a function f : V → {0, 1, 2, 3} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2, and every vertex u with f(u) = 1 is adjacent to at least one vertex assigned 2 or 3. The weight of f equals w(f) = ∑$_{v∈V}$ f(v). The double Roman domination number γ$_{dR}$(G) of a graph G equals the minimum weight of a double Roman dominating function of G. We obtain closed expressions for the double Roman domination number of generalized Petersen graphs P(5k, k). It is proven that γ$_{dR}$(P(5k, k)) = 8k for k ≡ 2, 3 mod 5 and 8k ≤ γ$_{dR}$(P(5k, k)) ≤ 8k + 2 for k ≡ 0, 1, 4 mod 5. We also improve the upper bounds for generalized Petersen graphs P(20k, k).

Keywords

double Roman domination;generalized Petersen graph;discharging method;graph cover;double Roman graph;

Data

Language:	English
Year of publishing:	2022
Typology:	1.01 - Original Scientific Article
Organization:	UL FS - Faculty of Mechanical Engineering
UDC:	519.17
COBISS:	93020931
ISSN:	2227-7390
Views:	153
Downloads:	60
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	dvojna rimska dominacija;posplošeni Petersonovi grafi;pokritja grafov;
Type (COBISS):	Article
Pages:	str. 1-19
Volume:	ǂVol. ǂ10
Issue:	ǂiss. ǂ1
Chronology:	Jan. 2022
DOI:	10.3390/math10010119
ID:	14305981