GFact | Meaning of this equation (L = (n-1)*I + 1) in n-ary Tree

Following relationship holds in any n-ary tree in which every node has either 0 or n children. L = (n-1)*I + 1 Where L is the number of leaf nodes and I is the number of internal nodes. Proof: The tree is n-ary tree. Assume it has T total nodes, which is sum of internal nodes (I) and leaf nodes (L). A tree with T total nodes will have (T - 1) edges or branches. In other words, since the tree is n-ary tree, each internal node will have n branches contributing total of n*I internal branches. Therefore we have the following relations from the above explanations, n*I = T - 1 L + I = T From the above two equations, it is easy to prove that L = (n - 1) * I + 1. Thanks to venki for providing the proof.