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 . Give examples or arguments to support your conclusions. The Minimal Connector Problem Suppose some real-life situation is modeled by a graph G with weights assigned to its edges. A possible pictorial representation of a graph with weights is shown below.