  The Johnson graph $J(n,i)$ is defined to the graph whose vertex set is the
set of all $i$-element subsets of $\{1,\ldots,n\}$, and two vertices are joined
whenever the cardinality of their intersection is equal to $i-1$. In Ramras and
Donovan [\emph{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
$S_n \times \langle T \rangle$, where $T$ is the complementation map $A \mapsto
\{1,\ldots,n\} \setminus A$. 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.
