No, it does not. It'll evolve when you trade it.
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Graveler does not evolve by a stone (or by a level). In order for Graveler to evolve, you have to trade Graveler over to another game.
No, it evolves by being traded.
Here are all of the Pokemon that can evolve using a Moon Stone:Nidorina uses a Moon Stone to evolve into Nidoqueen.Nidorino uses a Moon Stone to evolve into Nidoking.Clefairy uses a Moon Stone to evolve into Clefable.Jigglypuff uses a Moon Stone to evolve into Wigglytuff.Skitty uses a Moon Stone to evolve into Delcatty.Munna uses a Moon Stone to evolve into Musharna.
you cant evolve eevee with a moon stone
Graveler will only evolve when you trade it to someone.