Graphs Activity – Minimum Spanning Trees 1
Start
0
Starting with the vertex labeled “Start”, mark the minimum number of edges required to connect all vertices in the
graph.
Graphs Activity – Minimum Spanning Trees 2
Start
This is the same graph as before, but now each edge has a different cost that you pay if you use it. As before, start
with the vertex labeled “Start”, and mark the edges required to connect all vertices in the graph such that the total cost
of using these edges is as small as possible.
Graphs Activity – Minimum Spanning Trees 3
Start 2
Start 1
This is the same graph as before. It is also repeated on the next page. Choose a partner and work together on
connecting all vertices with the set of edges that has the least total cost. If finding the set of edges with the least total
cost is not possible, try to make the cost of the set of edges that you use as small as possible. One of you should work
on this page and start with the vertex labeled “Start 1”, and the other should work on the next page and start with the
vertex labeled “Start 2”. Before you begin, discuss how you will coordinate so that you finish the work quickly and still
find a set of edges with low total cost.
Graphs Activity – Minimum Spanning Trees 4
Start 2
Start 1
Continued from last page. Start with the vertex labeled “Start 2”.
Graphs Activity – Minimum Spanning Trees 5
Find the set of edges with the least total cost that connects all the vertices in this graph.
Graphs Activity – Traveling Salesman Problem
Start
A salesman needs to visit 6 stores in one day. In the graph above, each vertex represents a store. Each edge
represents a road connecting two stores, with the number on the edge representing the length of the road. The
salesman starts at store A and must return to store A at the end of the day. Find the best route that the salesman can
take, so that he travels the least distance and still visits all stores and returns to store A.