An engine includes an air intake system, an exhaust system, a single-cylinder-sourced EGR system, an exhaust sensor that is disposed to monitor exhaust gas from the single one of the cylinders, and a diverter valve. A controller includes an instruction set that executable to determine operation of the engine in a fuel cut-off mode, discontinue fuel flow to the single one of the cylinders, divert exhaust gas from the single one of the cylinders to the air intake system, determine an airflow, temperature, and an equivalence ratio of the diverted exhaust gas from the single one of the cylinders, determine a mass flowrate of oxygen in the diverted exhaust gas, integrate the mass flowrate of oxygen in the diverted exhaust gas, and discontinue the diverting of the exhaust gas from the single one of the cylinders when the integrated mass flowrate of oxygen is greater than a threshold value.