https://file.aiquickdraw.com/mathbot/file/1726107315172a6m5tf4c.jpg

In this graph, we are looking for a cycle, which is a closed loop in the graph where each vertex (point) is visited exactly once before returning to the starting point.

Let's examine the answer choices:

- **A: G – P – C – F – P – G**  
  This path revisits vertex \( P \) before completing the cycle, so it is not a valid cycle.

- **B: F – G – P – G – H – F**  
  This path revisits vertex \( G \) before completing the cycle, so it is also not a valid cycle.

- **C: S – C – P – F – C – S**  
  This path visits vertices \( S \), \( C \), \( P \), \( F \), and returns to \( S \), completing a cycle without revisiting any vertices prematurely. This is a valid cycle.

- **D: P – F – H – G – F – P**  
  This path revisits vertex \( F \) before completing the cycle, so it is not a valid cycle.

- **E: C – F – H – G – P – C**  
  This path visits vertices \( C \), \( F \), \( H \), \( G \), \( P \), and returns to \( C \), completing a cycle. This is another valid cycle.

So, the correct answers are **C** and **E**.

Would you like further details or explanations about cycles in graphs?

Here are some follow-up questions you might find interesting:
1. What is the definition of a cycle in graph theory?
2. How do cycles relate to Eulerian and Hamiltonian paths?
3. What are the real-world applications of cycle detection in graphs?
4. What types of algorithms are used to find cycles in graphs?
5. Can a graph contain multiple distinct cycles? If so, how are they found?

**Tip:** A simple cycle is one where no vertex (except the starting and ending vertex) is repeated within the loop!

The graph shows pathways linking animals on a farm. Which of the following represents a cycle in the graph?

Learn how to identify cycles in a graph through an example of pathways linking animals on a farm. This problem involves core graph theory concepts, particularly understanding cycles, and is suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation