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Question 1 of 4
Using the given network, which of the following sequences is a circuit?
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Types of Paths and Cycles
Walk : Walk : can be repeated .
Trail : Trail : can be repeated .
Path : Path : can not be repeated .
Cycle : Cycle : Starts and ends at the same vertex and both vertices and edges can not be repeated .
Circuit : 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 A - D - E - C - B - E - A
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 A - D - E - C - B - E - A circuit of the given network.
A − D − E − C − B − E − A A - D - E - C - B - E - A
Question 2 of 4
Using the given network, which of the following sequences is a trail?
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Types of Paths and Cycles
Walk : Walk : can be repeated .
Trail : Trail : can be repeated .
Path : Path : can not be repeated .
Cycle : Cycle : Starts and end at the same vertex and both vertices and edges can not be repeated .
Circuit : 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 - E - C - D - E - A A − B − E − C − E A - B - E - C - E A − D − C − B − A − D A - D - C - B - A - D not trails because they have repeating edges.
Only the sequence A − E − B − C − D − E − C A - E - B - C - D - E - C
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 A - E - B - C - D - E - C trail of the given network.
A − E − B − C − D − E − C A - E - B - C - D - E - C
Question 3 of 4
Using the given network, which of the following sequences is a path?
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Types of Paths and Cycles
Walk : Walk : can be repeated .
Trail : Trail : can be repeated .
Path : Path : can not be repeated .
Cycle : Cycle : Starts and end at the same vertex and both vertices and edges can not be repeated .
Circuit : 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 - E - C - D - E - A A − B − E − C − E A - B - E - C - E A − D − C − B − A − D A - D - C - B - A - D not paths because they have repeating edges.
Only the sequence A − B − D − C − E A - B - D - C - E
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 A - B - D - C - E path of the given network.
Question 4 of 4
Using the given network, which of the following sequences is a trail?
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Types of Paths and Cycles
Walk : Walk : can be repeated .
Trail : Trail : can be repeated .
Path : Path : can not be repeated .
Cycle : Cycle : Starts and end at the same vertex and both vertices and edges can not be repeated .
Circuit : 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 A − B − C − D − E A - B - C - D - E A − E − C − B − E A - E - C - B - E not cycles because they do not start and end on the same vertex.
Only the sequence C − E − D − C C - E - D - C
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 C - E - D - C cycle of the given network.
