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A note on the automorphism groups of Johnson graphs (1702.02568v4)
Published 8 Feb 2017 in math.CO and math.GR
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 \neq 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.