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Bee_see

  • one year ago

I was wondering if someone could check my answers for these problems: 1) Construct a simple graph G with all of the following properties: • G is connected. • G contains an edge whose removal disconnects G. • Every vertex of G has degree equal to 5.

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  1. Bee_see
    • one year ago
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    |dw:1442027403524:dw|

  2. jim_thompson5910
    • one year ago
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    I count 6 edges connected to these vertices (circled) |dw:1442027885574:dw|

  3. Bee_see
    • one year ago
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    or

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  4. Bee_see
    • one year ago
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    Oh, ok. So I just erase one line ?

  5. jim_thompson5910
    • one year ago
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    but then the outer vertices would only have 4 edges

  6. Bee_see
    • one year ago
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    Oh, that's right. Do I use the 2nd graph I have instead?

  7. jim_thompson5910
    • one year ago
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    that won't work either because of the same reason as above that bridge edge makes 2 nodes have 6 connecting edges

  8. jim_thompson5910
    • one year ago
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    this seems to work though |dw:1442028587295:dw|

  9. jim_thompson5910
    • one year ago
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    |dw:1442028753021:dw| the number in each circle represents the degree of each node

  10. Bee_see
    • one year ago
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    where is the curved not allowed to be plugged in?

  11. jim_thompson5910
    • one year ago
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    what do you mean?

  12. Bee_see
    • one year ago
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    I was trying to do this problem: Construct a simple graph on 6 vertices with 12 edges that does not contain K4 as a subgraph. and I did a graph like...|dw:1442028768219:dw|

  13. Bee_see
    • one year ago
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    I was told this was impossible to do.

  14. jim_thompson5910
    • one year ago
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    so I'm reading that K4 is a complete graph with 4 vertices shown on page 3 of this pdf http://www.dehn.wustl.edu/~blake/circles/talks/2009-jan18-Russ_Woodroofe-Graph_Theory.pdf is that the notation your teacher is using?

  15. Bee_see
    • one year ago
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    Oh, I did the problem. I was just asking about the curves. Is there a rule in which they can't be used for the graphs?

  16. jim_thompson5910
    • one year ago
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    I'm still not sure what you mean? In my drawing? or the one you posted?

  17. Bee_see
    • one year ago
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    in general.

  18. Bee_see
    • one year ago
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    Maybe I heard wrong...

  19. jim_thompson5910
    • one year ago
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    the edges can be curved, yes http://www.math.uvic.ca/faculty/gmacgill/guide/M222Graphs.pdf quoting that PDF ` Graphs are usually represented pictorially with a point (or dot) in the plane corresponding to each vertex and a line segment (or curve of some sort) joining the corresponding points for each pair of adjacent vertices.`

  20. Bee_see
    • one year ago
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    Hmm, can you check another problem for me?

  21. jim_thompson5910
    • one year ago
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    alright

  22. Bee_see
    • one year ago
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    2) Find a cycle of length 20 in the following graph:

  23. Bee_see
    • one year ago
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    Since it's a cycle, I'm sure it's supposed to return to its starting point, no?

  24. jim_thompson5910
    • one year ago
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    yeah you have to make a circuit and not repeat vertices

  25. jim_thompson5910
    • one year ago
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    so they want you to find a circuit with 20 edges where you don't repeat vertices

  26. jim_thompson5910
    • one year ago
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    your answer looks great

  27. Bee_see
    • one year ago
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    Thank you for checking my answers.

  28. jim_thompson5910
    • one year ago
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    no problem

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