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Showing the Kneser graph is vertex transitive

  1. Nov 6, 2009 #1
    1. The problem statement, all variables and given/known data
    the kneser graph KG(n:k) is the graph whose vertices are all of the k-subsets of {1,2,...,n} with 2 vertices beign adjacent if they are disjoint.

    show KG(n:k) is vertex transitive


    2. Relevant equations

    a graph G is vertex transitive if for any 2 vertices x,y in G, there is an automorphism f:X-->Y st f(x)=y

    3. The attempt at a solution

    i know the aut exists, but how do i show its bijective?

    if i find the aut i can show that a permutation does exist so that f(x)= y
    so f(x1,...,xk) = (y1,...,yn)

    let my permutation be Z that map all the x's to all the y's

    Z (x1...xk others not x )
    (y1...yk others not y)

    please guide me through this, im confused..

    i also need to show its arc transitive:
    so for ex given any 2 pairs of vertices (say u1,v1 u2,v2) there is an aut f:v(g)-->v(g) such that f(u1)=u2 and f(v1)=u2
     
  2. jcsd
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