ormore vertices. Since the vertex ofdegree twois distinctfrom all other vertices, it serves as a root, and so every binary tree is a rooted tree. Below are given some properties of binary trees. Theorem 4.10 Every binary tree has an odd number of vertices. Proof Apart from the root, every vertex in a binary tree is of odd degree. We know that
A directed graph is acyclic if it contains no directed cycles. We call a directed acyclic graph a dag . Sometimes, we want to find a linear order of the vertices of a dag such that all edges in the dag go in the direction of the linear order.