For each of the following graphs, find the shortest path for the given start and end point and state its length:
Start at vertex F and end at vertex E.
Start at vertex E and end at vertex B.
Start at vertex E and end at vertex B.
Start at vertex X and end at vertex V.
Start at vertex T and end at vertex Z.
Consider the graph which shows the time in hours taken to travel between various country towns:
Find the least amount of time needed to travel between towns P and X.
State the route that would achieve this by listing the vertices in order.
A group is organizing a tour for the elderly in a park, ending with a picnic. The given graph displays the map of the park:
Calculate the path which gives the shortest distance from the start of the park at vertex A, to the picnic area at vertex J.
The given map shows all possible routes in Mohamad's town. Mohamad travels from his home to his friend's house on a daily basis.
If Mohamad's house is vertex C, and his friend's house is vertex I, determine the shortest path between the two houses.
A grocery store is known for its fast deliveries across the town as shown in the following map:
If the store is at vertex A, and a delivery has to be made to vertex H, determine the shortest path the driver should take.
The police department receives a call about a robbery in progress at a grocery store. The given graph shows the map of the town:
If the nearest police car is located at vertex D and the grocery store is at vertex I, determine the shortest route the police should take.
A mailman was allocated an area to deliver the mail to. The table represents the mail route and times in minutes between the houses:
Draw a graph to represent the information in the table.
Find the fastest time to cycle from house A to house E.
State the fastest route by listing the vertices in order.
| Starting House | Ending House | Time |
|---|---|---|
| A | B | 11 |
| A | F | 9 |
| A | G | 3 |
| B | F | 5 |
| B | C | 10 |
| C | E | 8 |
| C | G | 6 |
| D | E | 5 |
| D | G | 5 |
| E | G | 7 |
A rock band is planning a tour across several cities. The table represents the routes and distance between the cities at which they will be performing in kilometres:
Draw a graph to represent the information in the table.
Find the shortest distance for the rock band to travel from city A to city E.
State the shortest route by listing the vertices in order.
| Starting City | Ending City | Distance |
|---|---|---|
| A | C | 9 |
| A | F | 6 |
| B | E | 11 |
| B | F | 5 |
| C | D | 3 |
| C | F | 7 |
| E | D | 5 |
| E | F | 8 |