The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2)
A double Roman dominating function (DRDF) f on a given graph G is a mapping from V ( G ) to { 0 , 1 , 2 , 3 } in such a way that a vertex u for which f ( u ) = 0 has at least a neighbor labeled 3 or two neighbors both labeled 2 and a vertex u for which f ( u ) = 1 has...
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MDPI AG
2018-10-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/6/10/206 |
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| author | Huiqin Jiang Pu Wu Zehui Shao Yongsheng Rao Jia-Bao Liu |
| author_facet | Huiqin Jiang Pu Wu Zehui Shao Yongsheng Rao Jia-Bao Liu |
| author_sort | Huiqin Jiang |
| collection | DOAJ |
| description | A double Roman dominating function (DRDF) f on a given graph G is a mapping from V ( G ) to { 0 , 1 , 2 , 3 } in such a way that a vertex u for which f ( u ) = 0 has at least a neighbor labeled 3 or two neighbors both labeled 2 and a vertex u for which f ( u ) = 1 has at least a neighbor labeled 2 or 3. The weight of a DRDF f is the value w ( f ) = ∑ u ∈ V ( G ) f ( u ) . The minimum weight of a DRDF on a graph G is called the double Roman domination number γ d R ( G ) of G. In this paper, we determine the exact value of the double Roman domination number of the generalized Petersen graphs P ( n , 2 ) by using a discharging approach. |
| first_indexed | 2024-12-14T15:00:48Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-14T15:00:48Z |
| publishDate | 2018-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f94f8fa401644cb9902cf1c7443d36d72022-12-21T22:56:50ZengMDPI AGMathematics2227-73902018-10-0161020610.3390/math6100206math6100206The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2)Huiqin Jiang0Pu Wu1Zehui Shao2Yongsheng Rao3Jia-Bao Liu4Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, Chengdu University, Chengdu 610106, ChinaInstitute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, ChinaInstitute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, ChinaInstitute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, ChinaSchool of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaA double Roman dominating function (DRDF) f on a given graph G is a mapping from V ( G ) to { 0 , 1 , 2 , 3 } in such a way that a vertex u for which f ( u ) = 0 has at least a neighbor labeled 3 or two neighbors both labeled 2 and a vertex u for which f ( u ) = 1 has at least a neighbor labeled 2 or 3. The weight of a DRDF f is the value w ( f ) = ∑ u ∈ V ( G ) f ( u ) . The minimum weight of a DRDF on a graph G is called the double Roman domination number γ d R ( G ) of G. In this paper, we determine the exact value of the double Roman domination number of the generalized Petersen graphs P ( n , 2 ) by using a discharging approach.http://www.mdpi.com/2227-7390/6/10/206double Roman dominationdischarging approachgeneralized Petersen graphs |
| spellingShingle | Huiqin Jiang Pu Wu Zehui Shao Yongsheng Rao Jia-Bao Liu The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2) Mathematics double Roman domination discharging approach generalized Petersen graphs |
| title | The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2) |
| title_full | The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2) |
| title_fullStr | The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2) |
| title_full_unstemmed | The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2) |
| title_short | The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2) |
| title_sort | double roman domination numbers of generalized petersen graphs p n 2 |
| topic | double Roman domination discharging approach generalized Petersen graphs |
| url | http://www.mdpi.com/2227-7390/6/10/206 |
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