Q77

A binary tree with $n > 1$ nodes has $n_1$, $n_2$ and $n_3$ nodes of degree one, two and three respec­tively. The degree of a node is defined as the number of its neighbours. Starting with the above tree, while there remains a node $v$ of degree two in the tree, add an edge between the two neighbours of $v$ and then remove $v$ from the tree. How many edges will remain at the end of the process?