Is it permissible to bring children to the graveyard, is there a specific age for that, and what is the ruling of Islamic law on this matter?

The Prophet, may Allah bless him and grant him peace, commanded visiting graves for admonition and remembering the Hereafter, as he said: "I had forbidden you from visiting graves, but now visit them, for in visiting them there is a reminder." If the child is discerning, there is no objection to him visiting graves. However, if he is not discerning, there is no need for that.