Game on Tree

You are given a tree with $n$ vertices numbered $1, 2, \ldots, n$. There are two players Alice and Bob who play a game on this tree, taking turns alternatively. Alice starts. In their turn, a participant has to remove a leaf (and the edge adjacent to it) from the tree. A leaf is a node with degree $1$. Please note that the tree changes with the game progressing, and a node which is not a leaf in