COMMUTER FLC HAS PROP STRIKE TXWY LIGHT DURING TAXI TO GATE. VIBRATION CAUSES SHUTDOWN OF 1 ENG. ACFT WAS ABLE TO TAXI TO RAMP.

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UPON LNDG ON RWY 19R AT XV40; WE WERE ADVISED 'R ON RWY 25L; R TXWY E; GRD 8 ON TXWY E.' NEITHER ANY RWY LIGHTS NOR TXWY LIGHTS WERE LIT AT THE TIME. UPON TURNING ONTO TXWY E; WE FELT VIBRATION. FO ADVISED THAT WE HAD HIT TXWY LIGHT WITH R PROP. ACFT WAS BROUGHT TO COMPLETE STOP AND R ENG WAS SHUT DOWN; APPLYING MEMORY ITEM CHKLIST. WE ADVISED GND CTL ABOUT PROP IMPACT ON TXWY LIGHT; AND TAXIED TO RAMP. AFTER LNDG CHKLIST WAS COMPLETED. WE ADVISED COMPANY THAT WE REQUIRED SPOT X OR SPOT Y AND ASKED MAINT TO MEET AT ACFT. SHUTDOWN CHKLIST WAS COMPLETED. DISEMBARKATION WAS NORMAL; EXCEPT FOR 1 NON REVENUE PAX; NO ONE ELSE KNEW OF THE IMPACT. DISPATCH PERSONNEL AND MAINT CREW ARRIVED AT ACFT SHORTLY AFTER SHUTDOWN. CAUSES: FATIGUE AND STARVATION PLUS LACK OF AMBIENT LIGHT AND NON ILLUMINATION OF RWY AND TXWY LIGHTS CAUSED ERROR IN TURNING RADIUS. PREVIOUS NIGHT ARRIVED VERY LATE AT HOTEL IN MQT (XA45). AWAKENED XF00 BY FALSE FIRE ALARM AND COULD NOT GO BACK TO SLEEP. EXCEPT FOR BREAKFAST XJ30; UNABLE TO CONSUME ANY MEALS ALL DAY DUE TO DELAYS AND ACFT SWAPS. I HAD ADVISED DISPATCH 40 MINS EARLIER OR PRIOR TO ARR THAT I WAS TIRED AND STARVED AND WOULD NOT FLY REMAINING 3 LEGS. 3 LEGS REMAINING WERE CANCELED.