Proofs needed here: please write proofs with full explanations for the following two questions. Thank you so much!!!!

MCS 12.10: Note: a graph is a collection of vertices and a collection of edges between them. The degree of a vertex is the number of edges touching it. Let's say that a graph has "two ends" if it has exactly two vertices of degree 1 all its other vertices have degree 2. For example, here is one such graph