Griffiths missed the defeat at St Johnstone due to the ankle injury that forced him off early in the previous match against Rangers, while Adam has been out since the end of August with a groin problem.
Danny Mullen is also in contention for a return to the squad after being sidelined since sustaining an ankle injury against St Mirren in the opening league match of the campaign, but Alex Jakubiak is out after undergoing shoulder surgery.
Aberdeen have attacking reinforcements with Ryan Hedges back and Marley Watkins given a chance to play following a hamstring injury.
Midfielder Teddy Jenks is also available again after suspension.
Defender Andy Considine is out until the turn of the year following knee surgery.