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Graph Walk Classification: Is AFECA a Walk, Trail, Path, or Circuit?
Published on October 24, 2026
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Determine whether the walk AFECA in the given graph is a walk, trail, path, or circuit by checking for repeated edges and whether the start and end vertices match. Since all edges are distinct and the walk begins and ends at A, it is a closed trail, which is a circuit.
Question
how do i solve this
Answer
Step 1: Identify the edges traversed.
The walk AFECA uses the consecutive edges:
The walk AFECA uses the consecutive edges:
- A–F
- F–E
- E–C
- C–A
Step 2: Check for repeated edges.
All four edges are different, so no edge is repeated. This makes the walk a trail.
All four edges are different, so no edge is repeated. This makes the walk a trail.
Step 3: Check the start and end vertices.
The walk starts at A and ends at A, so it is closed. A closed trail is a circuit.
The walk starts at A and ends at A, so it is closed. A closed trail is a circuit.
Step 4: Choose the most specific description.
A circuit is a more specific description than a walk or a trail. The vertices F, E, and C are each visited once, so the walk is also a cycle, but “circuit” is the option given.
A circuit is a more specific description than a walk or a trail. The vertices F, E, and C are each visited once, so the walk is also a cycle, but “circuit” is the option given.
Final answer: a circuit