On the automorphism group of a Johnson graph

The Johnson graph J(n, i) is defined to the graph whose vertex set is the set of all i-element subsets of {1,.., n}, and two vertices are joined whenever the cardinality of their intersection is equal to i-1. In Ramras and Donovan [SIAM J. Discrete Math, 25(1): 267-270, 2011], it is conjectured that if n = 2i, then the automorphism group of the Johnson graph J(n,i) is S-n x < T >, where T is the complementation map A bar right arrow {1,..., n} \ A. We resolve this conjecture in the affirmative. The proof uses only elementary group theory and is based on an analysis of the clique structure of the graph.