**Properties of Binary Trees: A Non-Linear Data Structure**

*In particular, we want to find out the maximum number of nodes in a binary tree of depth k, and the number of leaf nodes and the number of nodes of degree two in a binary tree. We present both these observations as lemma.*

**Lemma 5.1 [Maximum number of nodes]:***(1)The maximum number of nodes on level i of a binary tree is 2*

^{i}-1, i >= 1*(2)The maximum number of nodes in a binary tree of depth k is 2*

^{k}- 1, k >= 1

**Lemma 5.2 [Relation between number of leaf nodes and nodes of degree 2]:***Nonempty binary tree, T, if n*

_{0}is the number of leaf nodes and n_{2}the number of nodes of degree 2, then n_{0}= n_{2}+ 1.

**Thanks**

**Mukesh Rajput**
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Thanks

Mukesh Rajput