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Double Roman graphs in P(3k, k)
ID
Shao, Zehui
(
Author
),
ID
Erveš, Rija
(
Author
),
ID
Jiang, Huiqin
(
Author
),
ID
Peperko, Aljoša
(
Author
),
ID
Wu, Pu
(
Author
),
ID
Žerovnik, Janez
(
Author
)
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https://www.mdpi.com/2227-7390/9/4/336
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Abstract
A double Roman dominating function on a graph G = (V, E) is a function f : V → {0, 1, 2, 3} with the properties that if f(u) = 0, then vertex u is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2, and if f(u) = 1, then vertex u 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 is the minimum weight of a double Roman dominating function of G. A graph is said to be double Roman if γ$_{dR}$(G) = 3γ(G), where γ(G) is the domination number of G. We obtain the sharp lower bound of the double Roman domination number of generalized Petersen graphs P(3k, k), and we construct solutions providing the upper bounds, which gives exact values of the double Roman domination number for all generalized Petersen graphs P(3k, k). This implies that P(3k, k) is a double Roman graph if and only if either k ≡ 0 (mod 3) or k ∈ {1, 4}.
Language:
English
Keywords:
double Roman domination
,
generalized Petersen graph
,
double Roman graph
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
FS - Faculty of Mechanical Engineering
Publication status:
Published
Publication version:
Version of Record
Year:
2021
Number of pages:
18 str.
Numbering:
Vol. 9, iss. 4, art. 336
PID:
20.500.12556/RUL-134471
UDC:
519.17(045)
ISSN on article:
2227-7390
DOI:
10.3390/math9040336
COBISS.SI-ID:
50563587
Publication date in RUL:
17.01.2022
Views:
1002
Downloads:
121
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Record is a part of a journal
Title:
Mathematics
Shortened title:
Mathematics
Publisher:
MDPI AG
ISSN:
2227-7390
COBISS.SI-ID:
523267865
Licences
License:
CC BY 4.0, Creative Commons Attribution 4.0 International
Link:
http://creativecommons.org/licenses/by/4.0/
Description:
This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Licensing start date:
08.02.2021
Secondary language
Language:
Slovenian
Keywords:
dvojna rimska dominacija
,
posplošeni Petersenovi grafi
,
dvojno rimski grafi
Projects
Funder:
Other - Other funder or multiple funders
Funding programme:
National Key Research and Development Program
Project number:
2017YFB0802300
Funder:
Other - Other funder or multiple funders
Funding programme:
Sichuan Province, Applied Basic Research
Project number:
2017JY0095
Funder:
ARRS - Slovenian Research Agency
Project number:
P1-0222
Name:
Algebra v teoriji operatorjev in finančna matematika
Funder:
ARRS - Slovenian Research Agency
Project number:
P2-0248
Name:
Inovativni izdelovalni sistemi in procesi
Funder:
ARRS - Slovenian Research Agency
Project number:
J1-1693
Name:
Sodobni in novi metrični koncepti v teoriji grafov
Funder:
ARRS - Slovenian Research Agency
Project number:
J1-1692
Name:
Barvanja, dekompozicije in pokritja grafov
Funder:
ARRS - Slovenian Research Agency
Project number:
J2-2512
Name:
Stohastični modeli za logistiko proizvodnih procesov
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