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The Italian Domination Numbers of Generalized Petersen Graphs P ( n ,3)

Author

Listed:
  • Hong Gao

    (Department of Mathematics, Dalian Maritime University, Dalian 116026, China)

  • Changqing Xi

    (Department of Mathematics, Dalian Maritime University, Dalian 116026, China)

  • Kun Li

    (Department of Mathematics, Dalian Maritime University, Dalian 116026, China)

  • Qingfang Zhang

    (Department of Mathematics, Dalian Maritime University, Dalian 116026, China)

  • Yuansheng Yang

    (School of Computer Science and Technology, Dalian University of Technology, Dalian 116024, China)

Abstract

An Italian dominating function of G is a function f : V ( G ) → { 0 , 1 , 2 } , for every vertex v such that f ( v ) = 0 , it holds that ∑ u ∈ N ( v ) f ( u ) ≥ 2 . The Italian domination number γ I ( G ) is the minimum weight of an Italian dominating function on G . In this paper, we determine the exact values of the Italian domination numbers of P ( n , 3 ) .

Suggested Citation

  • Hong Gao & Changqing Xi & Kun Li & Qingfang Zhang & Yuansheng Yang, 2019. "The Italian Domination Numbers of Generalized Petersen Graphs P ( n ,3)," Mathematics, MDPI, vol. 7(8), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:714-:d:255510
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    References listed on IDEAS

    as
    1. Lutz Volkmann, 2016. "Signed total Roman domination in graphs," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 855-871, October.
    2. Zepeng Li & Zehui Shao & Jin Xu, 2018. "Weak {2}-domination number of Cartesian products of cycles," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 75-85, January.
    Full references (including those not matched with items on IDEAS)

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