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Johnson graphs are a special class of undirected graphs defined from systems of sets. The vertices of the Johnson graph J {\displaystyle J} are the k {\displaystyle k} -element subsets of an n {\displaystyle n} -element set; two vertices are adjacent when the intersection of the two vertices contains {\displaystyle } -elements. Both Johnson graphs and the closely related Johnson scheme are named after Selmer M. Johnson.
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