Prove that every nontrivial tree has at least two vertices of degree 1 by filling in the details and completing the following argument: Let T be a nontrivial tree and let S be the set of all paths from one vertex to another in T. Among all the paths in S, choose a path P with a maximum number of edges. (Why is it possible m find such a P?) What can you say about the initial and final vertices of P? Why?
That there are at least two vertices of degree in every nontrivial tree by determining the path with maximum number of edges and the nature of the initial and final vertices of that path.
is a nontrivial tree which as a set that contains all the paths of the tree. Also. is the path that covers maximum number of edges.
A vertex of degree is called a terminal vertex or a leaf, and a vertex of degree is called an internal vertex.
Regarding the nontrivial tree , the set is formed with all possible paths in the tree. A path is said to be a walk between two different vertices without repeated vertices or repeated edges
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