Question

Show that a tree has exactly two vertices of degree one if and only if it is a path.

Answer 1

Any two vertices in G can be connected by a unique simple path.

G is acyclic, and a simple cycle is formed if any edge is added to G.

G is connected and has no cycles.

G is connected but would become disconnected if any single edge is removed from G.

G is connected and the 3-vertex complete graph K3 is not a minor of G.