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Thread: Graphs

  1. #1
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    Graphs

    1.https://prnt.sc/j555ck
    2.https://prnt.sc/j555ju

    Can anyone offer an explanation as to how I would go about doing these TWO questions?

    Really not sure.
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  2. #2
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    Re: Graphs

    Do you know the meanings of the words used here? For the second problem, If you know what an "Euler circuit" is, then you can just trace each of the given options to see which are Euler circuits.

    For the first problem, in option a, having traversed edge $e_5$ you cannot then immediately go to $e_6$. For option b, can you trace a path through those vertices in order? If so, noting that you start and end at $v_2$, what kind of path is that?
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    Re: Graphs

    Quote Originally Posted by HallsofIvy View Post
    Do you know the meanings of the words used here? For the second problem, If you know what an "Euler circuit" is, then you can just trace each of the given options to see which are Euler circuits.

    For the first problem, in option a, having traversed edge $e_5$ you cannot then immediately go to $e_6$. For option b, can you trace a path through those vertices in order? If so, noting that you start and end at $v_2$, what kind of path is that?
    So for the first problem , it would be option b then right? Which is known as an Euler Path? Its not a circuit because in a circuit all vertices should be even in this case it has two odd vertices in terms of number of degrees?
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    Re: Graphs

    Quote Originally Posted by HallsofIvy View Post
    Do you know the meanings of the words used here? For the second problem, If you know what an "Euler circuit" is, then you can just trace each of the given options to see which are Euler circuits.

    For the first problem, in option a, having traversed edge $e_5$ you cannot then immediately go to $e_6$. For option b, can you trace a path through those vertices in order? If so, noting that you start and end at $v_2$, what kind of path is that?
    For the second problem is the answer the first option?
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  5. #5
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    Re: Graphs

    Quote Originally Posted by doxion View Post
    So for the first problem , it would be option b then right? Which is known as an Euler Path? Its not a circuit because in a circuit all vertices should be even in this case it has two odd vertices in terms of number of degrees?
    The question said nothing about an Euler path or circuit (that would have to use each edge exactly once). It only asked if the given path was a "trail", "circuit", or "path". What are the differences between those?
    Last edited by HallsofIvy; Apr 18th 2018 at 04:05 AM.
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