k -Rainbow Domination Number of P 3 □ P n

Ying Wang, Xinling Wu, Nasrin Dehgardi, Jafar Amjadi, Rana Khoeilar and Jia-Bao Liu
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Ying Wang: Department of network technology, South China Institute of Software Engineering, Guangzhou 510990, 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

Mathematics, 2019, vol. 7, issue 2, 1-9

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 } .

Keywords: k-rainbow dominating function; k-rainbow domination number; grids (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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