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

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

Povzetek

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).

Ključne besede

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

Podatki

Jezik:	Angleški jezik
Leto izida:	2022
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FS - Fakulteta za strojništvo
UDK:	519.17
COBISS:	93020931
ISSN:	2227-7390
Št. ogledov:	153
Št. prenosov:	60
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Slovenski jezik
Sekundarne ključne besede:	dvojna rimska dominacija;posplošeni Petersonovi grafi;pokritja grafov;
Vrsta dela (COBISS):	Članek v reviji
Strani:	str. 1-19
Letnik:	ǂVol. ǂ10
Zvezek:	ǂiss. ǂ1
Čas izdaje:	Jan. 2022
DOI:	10.3390/math10010119
ID:	14305981