What is the greeting said at graves, and does it differ from the greeting of the Prophet, peace and blessings be upon him, and his Companions? And is saying "Peace be upon you, O Messenger of Allah" at his grave and "Peace be upon you, O people of the graves" upon entering the graveyard considered polytheism (shirk)?

It is recommended for men to visit graves to remember the Hereafter. It is sunnah (definition) for the visitor to greet the inhabitants of the graves and supplicate for their forgiveness and well-being.

As for visiting the grave of Prophet Muhammad (peace be upon him) and his two companions, it is legislated to greet them with respect and a lowered voice, adhering only to what has been reported from the Companions, such as saying: "Peace be upon you, O Messenger of Allah; peace be upon you, O Abu Bakr; peace be upon you, O my father." One may add to this some appropriate descriptions. This greeting is not polytheism; rather, it is a supplication for their safety from the dangers of what comes after death.