The Cartesian product of cycles with small 2-rainbow domination number

Zofia Stȩpień (), Lucjan Szymaszkiewicz () and Maciej Zwierzchowski ()
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Zofia Stȩpień: West Pomeranian University of Technology
Lucjan Szymaszkiewicz: Szczecin University
Maciej Zwierzchowski: West Pomeranian University of Technology

Journal of Combinatorial Optimization, 2015, vol. 30, issue 3, No 16, 668-674

Abstract: Abstract The concept of 2-rainbow domination of a graph $$G$$ G coincides with the ordinary domination of the prism $$G\Box K_{2}$$ G □ K 2 (see Brešar et al., Taiwan J Math 12:213–225, 2008). Hence $$\gamma _{r2}(C_{m}\Box C_{n})\ge \frac{mn}{3}$$ γ r 2 ( C m □ C n ) ≥ m n 3 . In this paper we give full characterization of graphs $$C_m\Box C_n$$ C m □ C n with $$\gamma _{r2}(C_{m}\Box C_{n}) = \frac{mn}{3}$$ γ r 2 ( C m □ C n ) = m n 3 .

Keywords: Domination; Rainbow domination; Cartesian product of graphs; 05C69 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10878-013-9658-0

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