Walk:Walk: Both vertices and edges can be repeated.
Trail:Trail: Only vertices can be repeated.
Path:Path: Both vertices and edges 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-AA−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-AA−D−E−C−B−E−A is a circuit of the given network.
A-D-E-C-B-E-AA−D−E−C−B−E−A
Question 2 of 4
2. Question
Using the given network, which of the following sequences is a trail?
Path: Both vertices and edges can not be repeated.
Cycle:Starts and end at the same vertex and both vertices and edges can not be repeated.
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.
