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dan815

  • one year ago

How many cycles exist in a K5 graph with one edge missing? are all K5 graphs with one edge missing isomorphic? Definitions a Kn graph is a graph with n vertices and all vertices are connected to each other (total number of edges possible with n vertices, nchoose2) a cycle has to start and end with the same vertex, and can only intersect all other vertices only once

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  1. dan815
    • one year ago
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    i was thinking of solving this more combinatorically

  2. dan815
    • one year ago
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    but id have to first know if all k5 graphs with 1 edge missing is infact isomorphic,

  3. dan815
    • one year ago
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    |dw:1442452514625:dw|

  4. dan815
    • one year ago
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    oh ofcourse xD

  5. dan815
    • one year ago
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    okay so combinatorically i was thinking lets take every possible permutations 5! Total different cycles of 5 for k5 graph 5!/5 Total different cycles of 4 for k5 5!/4 Total different cycles of 3 for k5 5!/(2!*3) now from each case we must subtract where a certain edge is happening like since k5 is missing 1 edge then for example vertex 2 and 5 cannot appear each other, as going from 2 to 5 or from 5 to 2 is possible in a cycle

  6. dan815
    • one year ago
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    |dw:1442452762542:dw|

  7. dan815
    • one year ago
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    m thinking of every permutation as being around a round table to make it look like a cycle, thats why i am dividing by the length of the cycle

  8. dan815
    • one year ago
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    |dw:1442452906788:dw|

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