The Automorphism Group of a Johnson Graph

Abstract

Using an analysis of the clique structure and only the most elementary group theory, we determine the automorphism group of the Johnson graph $J(n,i)$, for $n\neq2i$. Although this is a special case of results of Jones [European J. Combin., 26 (2005), pp. 417-435], unlike his proof, ours uses no heavy group-theoretic machinery. We make a conjecture for the case $n=2i$.