- #1
a1010711
- 9
- 0
Homework Statement
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
Homework 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
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, I am 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