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For given $m<n$, consider the graph having as its nodeset the $m$-element subsets of $\{1,2,...,n\}$, with edges joining all pairs of nodes that have $m-1$ elements in common.

Is there an established name for that graph?

The above graph has the same nodes as the corresponding Kneser graph, but its edges differ: its node valency is $(n-m)m$, while the Kneser graph's node valency is $\left(n-m\atop m\right)$.

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    $\begingroup$ en.wikipedia.org/wiki/Johnson_graph $\endgroup$ – Ed Pegg Mar 16 '16 at 20:30
  • $\begingroup$ Settled. I just was told that such a graph is a "Johnson graph". Oops, Ed Pegg also posted the same information - thank you very much! $\endgroup$ – Goswin Mar 17 '16 at 9:50
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The graph is called a Johnson graph.

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