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The vertices of G are the k-subsets of some set of size n. Two k-subsets are connected by an edge of G if their symmetric difference is of size 2. The integers n and k are chosen so that the graph is not trivial.

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up vote 5 down vote accepted

That's the Johnson graph:

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Thank you for info. Is it known if those graphs are Hamiltonian? – w g Apr 21 '12 at 8:05
Yes, they are. The key word is combinatorial gray codes, see for example section 4 in – Thomas Kalinowski Apr 21 '12 at 10:22

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