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k-Rainbow Domination Number of P3Pn

Department of network technology, South China Institute of Software Engineering, Guangzhou 510990, China
Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
South China Business College, Guang Dong University of Foreign Studies, Guangzhou 510545, China
Department of Mathematics and Computer Science, Sirjan University of Technology, Sirjan 7813733385, Iran
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 5375171379, Iran
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Author to whom correspondence should be addressed.
Mathematics 2019, 7(2), 203;
Received: 12 January 2019 / Revised: 5 February 2019 / Accepted: 19 February 2019 / Published: 21 February 2019
(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)
PDF [249 KB, uploaded 21 February 2019]


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 } . View Full-Text
Keywords: k-rainbow dominating function; k-rainbow domination number; grids k-rainbow dominating function; k-rainbow domination number; grids

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Wang, Y.; Wu, X.; Dehgardi, N.; Amjadi, J.; Khoeilar, R.; Liu, J.-B. k-Rainbow Domination Number of P3Pn. Mathematics 2019, 7, 203.

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