On 2-rainbow domination of generalized Petersen graphs

Abstract Let γ r 2 ( G ) be the 2-rainbow domination number of a graph G . In our work, we solve an open question for 2-rainbow domination number of general Petersen graphs P ( n , k ) . In addition, we proved that γ r 2 ( P ( n , k ) ) = n for n ≤ 12 , γ r 2 ( P ( n , 1 ) ) = n for n ≥ 5 , and γ r 2 ( P ( 2 k + 2 , k ) ) = 2 k + 2 for k ≥ 2 .

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