The Johnson graph \(J(d,r)\) is unique if \((d,r)\neq (2,8)\) (Q1072567)

For any positive integer \(r\) set \(S_r=\{1,2,\dots,r\}\). The Johnson graph \(J(d,r)\) \((2\leq 2d\leq r)\) is the graph whose vertex set consists of all subsets of \(S_r\) of order \(d\), with vertices adjacent if their intersection has order \(d-1\). The author proves that the Johnson graph \(J(d,r)\) is the unique distance-regular graph with its own intersection numbers if \((d,r)\neq (2,8)\).