Therefore the forest has, This concludes the proof of the corollary. Every finite tree on two or more vertices has at least two vertices of degree one. If every vertex had degree 2 or greater, then the average degree of the vertices would be greater than or equal to 2. Since the average degree is less than 2, at least one vertex must have degree 1. The proof of the corollary guarantees that there is at least one vertex with degree 1.
G is any subgraph of G that is a tree.
A sub-forest is any subgraph of G that is a forest. If G is a connected graph, then a spanning tree for G is any subgraph of G that is a tree, and includes every vertex of G . Most graphs have more than one spanning tree. Try to think up examples or arguments to support your conclusions. That maximum distance is called the radius of G .