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Graph: difference between cycle & circuit

  1. Apr 20, 2016 #1
    1. The problem statement, all variables and given/known data
    What is the difference between a cycle & a circuit? (Definition not reqd, guidance reqd with the figure attached)

    2. Relevant equations

    No
    3. 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
     
  2. jcsd
  3. Apr 20, 2016 #2

    andrewkirk

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    Gold Member

    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
     
  4. Apr 20, 2016 #3
    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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