Graph: difference between cycle & circuit

  • Engineering
  • Thread starter zak100
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  • #1
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Homework Statement


What is the difference between a cycle & a circuit? (Definition not reqd, guidance reqd with the figure attached)

Homework Equations



No

The Attempt at a Solution


See the attached figure. According to this figure the walk AB, BC, CE, EF, FD, DA represents a cycle or not because we have a repeated vertex B?? (in my view its not a cycle because we have a repeated vertex in the middle).However it represents a circuit because there is no repeated edge.
Some body please guide me whether i am correct or not & give an example of cycle from the figure. Sorry for the picture not fitting with size. I have created it on paint & then saved it but i dont know how to get rid of extra white space.

Zulfi.
cycle & circuit diff2.png
 

Answers and Replies

  • #2
andrewkirk
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Both cycles and circuits are closed paths, meaning they end at the same vertex as where they started.
For a circuit, vertices may be repeat but not edges.
For a cycle, neither edges nor vertices may repeat (except that the start vertex is the same as the finish vertex).
Hence all cycles are circuits, but not vice versa.

The path listed above is a cycle (and hence also a circuit).
Why do you think it has a repeated vertex? As I read your post it goes ABCEFDA, so there are no repeated vertices (there are six vertices and six edges).

An example of a circuit that is not a cycle would be a figure eight, such as DBCDAFD
 
  • #3
462
11
Hi,
Thanks. Good Answer.
<Why do you think it has a repeated vertex? >

Actually i was using the whole edge. Now i know that i have to use only the vertices. i.e instead of AB, BC, CE, EF, FD, DA, i have to write only:
ABCEFDA.

Zulfi.
 

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