Identify Paths and Cycles
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Question 1 of 4
1. Question
Using the given network, which of the following sequences is a circuit?
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Types of Paths and Cycles
`\text(Walk):` Both vertices and edges can be repeated.`\text(Trail):` Only vertices can be repeated.`\text(Path):` Both vertices and edges can not be repeated.`\text(Cycle):` Starts and ends at the same vertex and both vertices and edges can not be repeated.`\text(Circuit):` Starts and ends at the same vertex and only vertices can be repeated.Since we are looking for a circuit, we can start by finding a sequence that starts and end at the same vertex.
Only the sequence `A-D-E-C-B-E-A` fits this category.To check if this sequence is a circuit of the given network, draw a diagram and check if the sequence repeats the vertices only.
The sequence started and ended at the same vertex and only repeated vertices. Therefore, sequence `A-D-E-C-B-E-A` is a circuit of the given network.`A-D-E-C-B-E-A` -
Question 2 of 4
2. Question
Using the given network, which of the following sequences is a trail?
Hint
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Types of Paths and Cycles
`\text(Walk):` Both vertices and edges can be repeated.`\text(Trail):` Only vertices can be repeated.`\text(Path):` Both vertices and edges can not be repeated.`\text(Cycle):` Starts and end at the same vertex and both vertices and edges can not be repeated.`\text(Circuit):` Starts and end at the same vertex and only vertices can be repeated.Since we are looking for a trail, we can start by finding a sequence that does not repeat an edge.The sequences `A-E-C-D-E-A`, `A-B-E-C-E` and `A-D-C-B-A-D` are not trails because they have repeating edges.
Only the sequence `A-E-B-C-D-E-C` fits the category of a trail.To check if this sequence is a trail of the given network, draw a diagram and check if the sequence repeats the vertices only.
The sequence only repeats vertices. Therefore, sequence `A-E-B-C-D-E-C` is a trail of the given network.`A-E-B-C-D-E-C` -
Question 3 of 4
3. Question
Using the given network, which of the following sequences is a path?
Hint
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Exceptional!
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Types of Paths and Cycles
`\text(Walk):` Both vertices and edges can be repeated.`\text(Trail):` Only vertices can be repeated.`\text(Path):` Both vertices and edges can not be repeated.`\text(Cycle):` Starts and end at the same vertex and both vertices and edges can not be repeated.`\text(Circuit):` Starts and end at the same vertex and only vertices can be repeated.Since we are looking for a path, we can start by finding a sequence that does not repeat a vertex or an edge.The sequences `A-E-C-D-E-A`, `A-B-E-C-E` and `A-D-C-B-A-D` are not paths because they have repeating edges.`A-B-C-D-E`
`A-D-C-E-C`
`A-B-C-B`
Only the sequence `A-B-D-C-E` fits the category of a path.To check if this sequence is a path of the given network, draw a diagram and check if the sequence does not repeat a vertex or an edge.
The sequence does not repeat any vertex or edge. Therefore, sequence `A-B-D-C-E` is a path of the given network.`A-B-D-C-E` -
Question 4 of 4
4. Question
Using the given network, which of the following sequences is a trail?
Hint
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Fantastic!
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Types of Paths and Cycles
`\text(Walk):` Both vertices and edges can be repeated.`\text(Trail):` Only vertices can be repeated.`\text(Path):` Both vertices and edges can not be repeated.`\text(Cycle):` Starts and end at the same vertex and both vertices and edges can not be repeated.`\text(Circuit):` Starts and end at the same vertex and only vertices can be repeated.Since we are looking for a cycle, we can start by finding a sequence that starts and ends at the same vertex and does not repeat a vertex or an edge.The sequences `A-B-C-D`, `A-B-C-D-E` and `A-E-C-B-E` are not cycles because they do not start and end on the same vertex.
Only the sequence `C-E-D-C` fits the category of a cycle.To check if this sequence is a cycle of the given network, draw a diagram and check if the sequence starts and end at the same vertex and does not repeat a vertex or an edge.
The sequence starts and end at the same vertex and does not repeat any vertex or edge. Therefore, sequence `C-E-D-C` is a cycle of the given network.`C-E-D-C`
Quizzes
- Vertices and Edges
- Degrees 1
- Degrees 2
- Degrees 3
- Drawing a Network 1
- Drawing a Network 2
- Completing a Table from a Network Diagram
- Network from Maps and Plans
- Identify Paths and Cycles
- Eulerian Trails and Circuits 1
- Eulerian Trails and Circuits 2
- Identify Spanning Trees
- Minimum Spanning Trees 1
- Minimum Spanning Trees 2
- Shortest Path 1
- Shortest Path 2