The Double Roman Domination Numbers of Generalized Petersen Graphs P ( n, 2)

Huiqin Jiang, Pu Wu, Zehui Shao, Yongsheng Rao and Jia-Bao Liu
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Huiqin Jiang: Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, Chengdu University, Chengdu 610106, China
Pu Wu: Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
Zehui Shao: Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
Yongsheng Rao: Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
Jia-Bao Liu: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China

Mathematics, 2018, vol. 6, issue 10, 1-11

Abstract: 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 ? 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.

Keywords: double Roman domination; discharging approach; generalized Petersen graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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