Abstract
Let I be a set of infinite cardinality α. For every cardinality β≤α the Johnson graphs Jβ and Jβ are the graphs whose vertices are subsets X⊂I satisfying |X|=β, |I∖X|=α and |X|=α, |I∖X|=β (respectively) and vertices X,Y are adjacent if |X∖Y|=|Y∖X|=1. Note that Jα=Jα and Jβ is isomorphic to Jβ for every β<α. If β is finite then Jβ and Jβ are connected and it is not difficult to prove that their automorphisms are induced by permutations on I. In the case when β is infinite, these graphs are not connected and we determine the restrictions of their automorphisms to connected components.
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