I need help with a graph theory questionb) Let T be a tree with more then one vertex, prove that T musthave atleast one vertex of degree 1 

Expert Answers
embizze eNotes educator| Certified Educator

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.