What is the total degree of a tree with n vertices? Why?
The total degree of tree with and give reason also.
The total degree of a tree with vertices.
First prove that the number of edges in graph is equal to , using induction method. Here is the number of vertices.
This is true for .
Let be a tree with vertices and be an edge with end vertices and .
That means that the path between is .
Therefore, deletion of disconnects .
Assume that consists of exactly two components namely .
There were no cycles to begin with, hence each component is a tree.
The tree is shown below.
Take as the number of vertices in respectively.
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