A binary tree can be recursively defined as follows.A single vertex is a binary tree. (This single vertex is the root of this binary tree.)If T1 and T2 are binary trees, then so is the result of the following construction.– Create a new vertex. (This vertex will become the root of the new binary tree.)– Add an edge between this new root vertex and the roots of T1 and T2.Prove the following for all binary trees:• Root vertices either have degree 0 or 2 and are the only vertices with these degrees.The number of degree 1 vertices is 2 more than the number of degree 3 vertices.(Hint: It will be simpler to combine the two properties in a single proof.)
Level/Year: First year
Subject: Discrete Structures
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PhD in Theoretical Physics