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Bee_see

  • one year ago

Are the following pairs of graphs isomorphic? If they are isomorphic, label the vertices to show an isomorphism. If they are not isomorphic, explain why not; specifically, find a graph property that is not shared by both graphs. It suffices for this problem to merely state the graph properties–you do not need to prove rigorously that they hold.

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  1. Bee_see
    • one year ago
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  2. anonymous
    • one year ago
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    At first I thought it said Islamophobic so I was getting my caps lock ready|dw:1440778755730:dw|

  3. freckles
    • one year ago
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    looks like we need to consider the degree of the nods |dw:1440782933158:dw|

  4. freckles
    • one year ago
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    \[\deg(A)=3 \\ \deg(B)=3 \\ \deg(C)=3 \\ \deg(D)=3 \\ \deg(E)=2 \\ \deg(F)=2 \\ \deg(G)=2 \\ \deg(H)=2 \\ \deg(I)=4 \\ ... \\ \deg(1)=3 \\ \deg(2)=3 \\ \deg(3)=3 \\ \deg(4)=3 \\ \deg(5)=2 \\ \deg(6)=2 \\ \deg(7)=2 \\ \deg(8)=2 \\ \deg(9)=4\]

  5. freckles
    • one year ago
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    so we have degree numbers match up

  6. freckles
    • one year ago
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    that is probably not enough information like if the degree things didn't match up we could say it isn't isomorphic but I think we might need a bit more now

  7. Bee_see
    • one year ago
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    Ok.

  8. freckles
    • one year ago
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    |dw:1440783764768:dw| looks like these graphs would be the same if you rotate the inner square and make that inner square thing into an X

  9. Bee_see
    • one year ago
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    I don't think the professor would like to rotate it...

  10. freckles
    • one year ago
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    |dw:1440783799919:dw| hmm but this shows there is an edge going from A to E and we didn't previously have that

  11. freckles
    • one year ago
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    so mapping A to 1 and E to 5 wouldn't work because A to E are not connected while 1 to 5 is

  12. freckles
    • one year ago
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    so appears these graphs are not isomorphic

  13. Bee_see
    • one year ago
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    why exactly did you rotate the square?

  14. freckles
    • one year ago
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    I was trying to see if the graphs would be the same if I reconstructed the first to try to look like the second but in reconstruction I noticed the information about the edges there

  15. freckles
    • one year ago
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    something easier for you might be to compare the number of edges from each

  16. Bee_see
    • one year ago
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    don't both have 12 edges though?

  17. freckles
    • one year ago
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    |dw:1440784272471:dw| nevermind