What is the ruling on reading the Quran at the grave, and is it considered an innovation? And what is better among that which is reported from the Prophet, peace and blessings be upon him, at the grave: reading the Quran or supplicating?

It has not been reported that the Prophet, peace and blessings be upon him, recited at the grave. Rather, what has been reported from him is supplicating for the deceased after burial or when visiting graves. He said when a Companion was buried: "Ask for forgiveness for your brother and ask for steadfastness for him, for indeed he is now being questioned."