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.
An example of an infinite tree, which has no vertex of degree .
Any tree that has more than one vertex has at least one vertex of degree .
Assume a graph with vertices .
Consider the following definitions:
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