CS 594 Graph Theory, Spring 2014 Homework 2
1. Draw a graph with a disconnected center, marking the eccentricity of each vertex.
2. How many spanning trees does labeled W5 contain? What about unlabeled W5?
3. What is the diameter and radius of the biclique Km,n?
4. Prove that if
2.1.11.)
has diameter at least 4, then
has diameter at most 2. (Hint: Use Theorem
5. Let T be a tree in which every vertex has degree 1 or degree k. Determine the possible values
of n(T).
6. Prove that if is a connected graph with n vertices, then
has exactly n edges.
has exactly one cycle if and only if
7. Explain how to use BFS (Breadth-First Search) to find the girth of a graph.