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k -Rainbow Domination Number of P 3 □ P n

Author

Listed:
  • Ying Wang

    (Department of network technology, South China Institute of Software Engineering, Guangzhou 510990, China
    Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China)

  • Xinling Wu

    (South China Business College, Guang Dong University of Foreign Studies, Guangzhou 510545, China)

  • Nasrin Dehgardi

    (Department of Mathematics and Computer Science, Sirjan University of Technology, Sirjan 7813733385, Iran)

  • Jafar Amjadi

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 5375171379, Iran)

  • Rana Khoeilar

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 5375171379, Iran)

  • Jia-Bao Liu

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

Abstract

Let k be a positive integer, and set [ k ] : = { 1 , 2 , … , k } . For a graph G , a k-rainbow dominating function (or kRDF ) of G is a mapping f : V ( G ) → 2 [ k ] in such a way that, for any vertex v ∈ V ( G ) with the empty set under f , the condition ⋃ u ∈ N G ( v ) f ( u ) = [ k ] always holds, where N G ( v ) is the open neighborhood of v . The weight of kRDF f of G is the summation of values of all vertices under f . The k-rainbow domination number of G , denoted by γ r k ( G ) , is the minimum weight of a kRDF of G . In this paper, we obtain the k-rainbow domination number of grid P 3 □ P n for k ∈ { 2 , 3 , 4 } .

Suggested Citation

  • Ying Wang & Xinling Wu & Nasrin Dehgardi & Jafar Amjadi & Rana Khoeilar & Jia-Bao Liu, 2019. "k -Rainbow Domination Number of P 3 □ P n," Mathematics, MDPI, vol. 7(2), pages 1-9, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:203-:d:208033
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