1. In the GraphD workshop applet, see if you can create a graph with a cycle that the Topo routine cannot identify. 2. Use the GraphW Workshop applet to find the minimum spanning tree of the graph...

1.
In the GraphD workshop applet, see if you can create a graph with a cycle that

the Topo routine cannot identify.

2.
Use the GraphW Workshop applet to find the minimum spanning tree of the

graph shown Train fares in Magnaguena.” Consider the graph

to be undirected; that is, ignore the arrows.

3.
Use the GraphDW Workshop applet to solve the shortest-path problem for the

graph in“Train fares in Magnaguena,” but derive new weights for

all the edges by subtracting those shown in the figure from 100.

4.
Draw a graph with five vertices and five edges. Then use pencil and paper to

implement Djikstra’s algorithm for this graph. Show the tree and the shortestpath

array at each step.