1 Answer | Add Yours
A tree is an acyclic, connected graph. If the graph has more than one vertex, and every vertex has at least degree two, then there must be a cycle which contradicts the given that the graph is a tree.
Any vertex of degree at least 2 is a cut vertex, and any nontrivial graph contains at least two vertices that are not cut vertices.
We’ve answered 319,436 questions. We can answer yours, too.Ask a question