Luffy knew that Dragon was the revolutionary, the most dangerous man in the world, his father. Two people have not talked to each other. In fact, their only conversation was when Dragon saved Luffy from being captured by the Smoker, and the only thing Luffy told him was "someone?" While his head was dropped to the ground by Smoker. It is possible that Dragon always cared about his son's life because Dragon saved Luffy at Loguetown and he always looked at the South China Sea where his family lived. Dragon seems to be expecting great things from Luffy, just like his grandfather. However, unlike Garp, Dragon seems to allow him to find his own place in the world. Luffy did not know anything about Dragon's work but he still knew and acknowledged that he was his son.