Distinguishing simple groups

Abstract

The distinguishing number $D(\Gamma )$ of a graph $\Gamma$ is the least size of a partition of the vertices of $\Gamma$ such that no non-trivial automorphism of $\Gamma$ preserves this partition. We show that if the automorphism group of a graph $\Gamma$ is simple, than $D(\Gamma )=2$. This is obtained by establishing the distinguishing number for all possible actions of simple groups.

arXiv admin note: text overlap with arXiv:1910.11806