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New results on singleton rainbow domination numbers of generalized Petersen graphs <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>(</mo><mi>c</mi><mi>k</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula> are given. Exact values are established for some infinite families, and lower and upper bounds with small gaps are given in all other cases.