* Summoning Conditions: "Grapha, Dragon Lord of the Dark World" can only be Special Summoned from your hand when you control no monsters, and only during your Main Phase.
* Timing: Special Summoning is a part of your Main Phase actions. You cannot perform Main Phase actions during your opponent's turn.
Therefore, while you can potentially meet the conditions for summoning Grapha during your opponent's turn (having no monsters on the field), you cannot actually perform the summon itself.
It's important to note that some cards or effects could potentially manipulate timing or allow for special summoning during your opponent's turn, but these would need to specifically circumvent the normal restrictions on summoning.