Give a vertex list/edge list definition of the following graph:
Give the adjacency matrix from the graph in the previous problem.
Give an example of a shortest path from vertex d to vertex
c in the previous graph.
In the previous graph, how many edges would you have to remove to
make a tree? Explain.
For each of the graphs below, find an Euler path or Euler circuit
if possible. If it's not possible, explain why.
For the planar multigraph shown below, verify that Euler's formula holds
(v-e+r = 2). Then draw the dual multigraph, and verify that Euler's
formula holds for the dual.
For each of the following pairs of graphs, determine whether or not they
are isomorphic. If they are, then give a mapping between the vertices that
preserves the edge list. If they are not, then prove it by finding a
specific difference that should be identical for isomorphic graphs.
Apply Dijkstra's algorithm to the weighted graph below to determine the
shortest distance from vertex a to each of the other six vertices in the
graph. Then give the actual shortest path from a to each of the other
six vertices that achieves that shortest distance.
Show in some way the details of the computation that you did in
Dijkstra's algorithm (for example, give a table like we did in class.)
