📚 Part 1: Understanding Walks and Circuits
1. Which of the following best defines a walk in a network?
A sequence of vertices and edges where vertices and edges cannot be repeated
A sequence of vertices and edges where vertices and edges may be repeated
A path that must start and end at the same vertex
A connection between two vertices only
2. Which of the following best defines a circuit in a network?
Any walk that visits all vertices exactly once
A walk that starts and ends at the same vertex and does not repeat any edge
A sequence where all edges must be repeated
A path between two different vertices
3. In a directed graph, what must be considered when identifying walks and circuits?
The colour of the vertices
The direction of the edges (arrows)
The size of the vertices
The number of edges only
4. Consider the triangle network with vertices A-B-C-A. This is an example of:
A walk only
A circuit only
Both a walk and a circuit
Neither a walk nor a circuit
✏️ Part 2: Analysing Network Diagrams
5. For the network path A-B-C-B-D, explain why this is a walk but not a circuit:
6. A delivery driver needs to plan a route that starts and ends at the same depot without using any street twice. What type of network path should they find?
Answer: ________________
7. In a weighted graph, the edges have numbers representing distances in kilometres. If you need to find the shortest circuit, what additional step must you take beyond identifying possible circuits?
8. List two real-world examples where understanding walks and circuits in networks would be useful:
Example 1: _________________________________________________
Example 2: _________________________________________________
🎯 Part 3: Problem Solving
9. A tourist wants to visit all attractions in a city and return to their hotel. The city map can be represented as a network where vertices are locations and edges are streets. Some streets are one-way (directed edges) and have different travel times (weights).
a) What type of network path should the tourist look for? ________________
b) Why might the tourist need to consider the direction of streets?
c) How would the tourist use the travel times (weights) to plan the best route?
10. Design a simple network problem: Create a scenario where someone needs to find either a walk or circuit in a network. Describe the situation and explain what type of path would be most suitable.
