Travelling Networks Worksheet

Name:

Date:

📖 Key Definitions - Network Travel Concepts

Understanding the Language of Networks:

Walk: A sequence of vertices and edges where you can repeat both vertices and edges. Think of it as any journey through the network - you can go back and forth as much as you like!

Trail: A walk where you cannot repeat edges, but you can repeat vertices. It's like walking through a city where you can visit the same intersection twice, but you can't use the same street twice.

Circuit: A special type of walk that starts and ends at the same vertex without repeating any edges. Perfect for round trips!

Cycle: A circuit where you don't repeat any vertices except the starting/ending vertex. This is the most efficient type of round trip.

1. Match each definition to the correct term:

Walk

Trail

Circuit

Cycle

Round trip with no repeated edges or vertices

Any journey - vertices and edges can be repeated

Round trip with no repeated edges

Journey with no repeated edges but vertices can repeat

2. Complete the following statements:

a) In a walk, vertices and edges _______ be repeated.

b) A circuit must start and end at the _______ vertex.

c) The difference between a circuit and a cycle is that a cycle cannot repeat _______.

d) In a trail, you cannot repeat _______ but you can repeat _______.

🔍 Part 2: Identifying Different Types of Network Journeys

3. Consider the triangle network with vertices A, B, C where each vertex connects to the other two. Classify each journey:

A-B-C-A is a:

Walk

Trail

Circuit

Cycle

A-B-A-C is a:

Walk only

Trail

Circuit

Cycle

A-B-C-A-B is a:

Walk only

Trail

Circuit

Cycle

4. In a path network A-B-C-D, identify what type of journey each sequence represents:

A-B-C-D: Type = _____________

A-B-C-B-D: Type = _____________

D-C-B-A: Type = _____________

A-B-C-D-C-B-A: Type = _____________

5. Draw a simple network diagram below that shows:

• A cycle with 4 vertices (label as vertices W, X, Y, Z)

• Mark one example of a trail that is not a cycle

🚚 Part 3: Delivery Route Problem

6. A delivery driver needs to plan routes through a neighbourhood network. The weighted graph below shows intersections (vertices) and streets (edges) with travel times in minutes:

Network: Depot(D) - Shop(S) - House1(H1) - House2(H2) - Depot(D)

Edge weights: D-S: 5 min, S-H1: 3 min, H1-H2: 4 min, H2-D: 6 min, D-H1: 8 min

a) List two different circuits starting and ending at the Depot (D):

b) Calculate the total travel time for each circuit you identified:

c) Which circuit would you recommend for the delivery driver and why?

7. Explain why the driver would prefer a circuit over just a walk when making deliveries: