I have read a book about a cyclops on an island and he was the son of Posiden, After that he finds lost greeks, The men had a plan and killed the cyclops because he wants to eat them all, The greeks used a huge stick to hit on his eye. If some human army from the 500B.C could kill a cyclops and I guess a dragon could kill one too.
But in the book afetr they killed him , The cyclops told his father, then put a curse on the leader, which we wanted to go back to his land for 10 years to live with his son and mother, but the god Posiden cursed Him and he could never see his family again. I said that, just to let you know, very sad book.