Diameter of a graph G is defined to be the length of the shortest walk from one vertex to another vertex. The diameter of the graph G is defined to be the maximum value that is the distance between two vertices in G.
What is the diameter of each of the following graphs?
Find an example graph G and an edge in G such that if we create a new graph H by deleting the edge from G, H is still connected and has the same diameter. Draw pictures of both G and H. Label the edge in your picture of G. In both pictures, indicate a pair of vertices such that the distance between them is the diameter of the graph.
Find an example of graph G and an edge in G such that if we create a new graph H by deleting the edge from G, H is still connected and has a larger diameter than G. Draw pictures of both G and H. Label the edge in your picture of G. In both pictures, indicate a pair of vertices such that the distance between them is the diameter of the graph.
Suppose G is a graph with 1000 vertices and that each vertex in G has a degree of 800. Show that the number of edges in G is exactly equal to 400,000.