let , the tree with degree max =2 ,
let , no of intenal nodes whose degree >1 =k
then no of pedent vertex = n-k
now as we know that no of edges in tree = n-1
by handshaking theorem ,
sum of degrees of each verteces = 2 * edges
now , 2*(k)+1*(n-k) = 2*(n-1) => k = (n-2)