Is this perfect information game played on graphs know/studied?Given a graph $G= (V,E)$, two players alternate picking an edge or an isolated node. If the player picks an edge $e = (u,v)$ the two nodes $u$ and $v$ are deleted along with their incident edges. If the player picks an isolated node, the node is deleted. The first player unable to move loses the game.What is the complexity of finding the winner?Any references to similar games?
Winning strategy of an edge or isolated vertex deletion game
reference request;combinatorial game theory