The automorphism group of the s -stable Kneser graphs

TORRES, PABLO

ADVANCES IN APPLIED MATHEMATICS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2017 vol. 89 p. 67 - 75

0196-8858

For $k,sgeq2$, the $s$-stable Kneser graphs are the graphs with vertex set the$k$-subsets $S$ of ${1,ldots,n}$ such that the circular distance between any two elements in $S$is at least $s$ and two vertices are adjacent if and only if the corresponding $k$-subsetare disjoint. Braun showed that for $ngeq 2k+1$ the automorphism group of the $2$-stable Kneser graphs (Schrijver graphs) is isomorphic to the dihedral group of order $2n$.In this paper we generalize this result by proving that for $sgeq 2$ and $ngeq sk+1$ the automorphism group of the $s$-stable Kneser graphs also is isomorphic to the dihedral group of order $2n$.