If graphs are allowed to have an infinite number of vertices and edges. then Lemma 10.4.1 is false. Give a counterexample that shows this. In other words. give an example of an “infinite tree” (a connected. circuit-free graph with an infinite number of vertices and edges) that has no vertex of degree 1.

To find:

An example of an infinite tree, which has no vertex of degree 1.

Given information:

Lemma

Concept used:

Any tree that has more than one vertex has at least one vertex of degree 1.

Graph:

Assume a graph with n vertices v0,v1,v2,v3,v4,.......,vn.

Consider the following definitions:

1. Connected graph: A graph is said to be connected graph if and only if, for any two given vertices in the graph, there exists a walk between those two vertices