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?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 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 `ADECBEA` 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 `ADECBEA` is a circuit of the given network.`ADECBEA` 
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 `AECDEA`, `ABECE` and `ADCBAD` are not trails because they have repeating edges.Only the sequence `AEBCDEC` 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 `AEBCDEC` is a trail of the given network.`AEBCDEC` 
Question 3 of 4
3. Question
Using the given network, which of the following sequences is a path?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 path, we can start by finding a sequence that does not repeat a vertex or an edge.The sequences `AECDEA`, `ABECE` and `ADCBAD` are not paths because they have repeating edges.`ABCDE``ADCEC``ABCB`Only the sequence `ABDCE` 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 `ABDCE` is a path of the given network.`ABDCE` 
Question 4 of 4
4. 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 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 `ABCD`, `ABCDE` and `AECBE` are not cycles because they do not start and end on the same vertex.Only the sequence `CEDC` 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 `CEDC` is a cycle of the given network.`CEDC`
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