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

Author

Listed:
  • 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)

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 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.

Suggested Citation

  • Huiqin Jiang & Pu Wu & Zehui Shao & Yongsheng Rao & Jia-Bao Liu, 2018. "The Double Roman Domination Numbers of Generalized Petersen Graphs P ( n , 2)," Mathematics, MDPI, vol. 6(10), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:10:p:206-:d:176046
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    References listed on IDEAS

    as
    1. Zehui Shao & Jin Xu & S. M. Sheikholeslami & Shaohui Wang, 2018. "The Domination Complexity and Related Extremal Values of Large 3D Torus," Complexity, Hindawi, vol. 2018, pages 1-8, July.
    2. H. Abdollahzadeh Ahangar & J. Amjadi & S. M. Sheikholeslami & L. Volkmann & Y. Zhao, 2016. "Signed Roman edge domination numbers in graphs," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 333-346, January.
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    Cited by:

    1. Darja Rupnik Poklukar & Janez Žerovnik, 2023. "Double Roman Domination: A Survey," Mathematics, MDPI, vol. 11(2), pages 1-20, January.
    2. Samadi, B. & Soltankhah, N. & Abdollahzadeh Ahangar, H. & Chellali, M. & Mojdeh, D.A. & Sheikholeslami, S.M. & Valenzuela-Tripodoro, J.C., 2023. "Restrained condition on double Roman dominating functions," Applied Mathematics and Computation, Elsevier, vol. 438(C).

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