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Groups and graphs

  1. Jun 2, 2009 #1
    Hi.

    Need help with following problem:

    Let R=(V,E) a regular graph with degree at least 1 and odd number of vertices.
    Let C=Aut(R) the transitive action on the set E of R.

    Prove C also transitive action on the set V of R.


    Anyone got any idea/tips?

    Thanks!
     
  2. jcsd
  3. Jun 6, 2009 #2
    Try assuming the contrary: that the action is not transitive on V. Deduce that R is bipartite. Contradiction. Am I missing something?
     
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