A note on the automorphism groups of Johnson graphs

Abstract

The Johnson graph $J(n,i)$ is defined as the graph whose vertex set is the set of all $i$-element subsets of $\{1,...,n\}$, and two vertices are adjacent 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 proved that if $n\ne 2i$, then the automorphism group of $J(n,i)$ is isomorphic with the group $Sym(n)$ and it is conjectured that if $n=2i$, then the automorphism group of $J(n,i)$ is isomorphic with the group $Sym(n)\times {\mathbb{Z}}_2$. In this paper, we will find these results by different methods. We will prove the conjecture in the affirmative.

Research paper, submitted

Cited by in corpus (2)

• Some algebraic properties of bipartite Kneser graphs
• A note on the automorphism group of the Hamming graph