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Mathematics 2019, 7(2), 203; https://doi.org/10.3390/math7020203

k-Rainbow Domination Number of P3Pn

1
Department of network technology, South China Institute of Software Engineering, Guangzhou 510990, China
2
Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
3
South China Business College, Guang Dong University of Foreign Studies, Guangzhou 510545, China
4
Department of Mathematics and Computer Science, Sirjan University of Technology, Sirjan 7813733385, Iran
5
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 5375171379, Iran
6
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
*
Author to whom correspondence should be addressed.
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)
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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 } . 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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