Distinguishing simple groups

2020/01/14 by Grech, Mariusz, Kisielewicz, Andrzej
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.06300

Abstract

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

Related

• Distinguishing actions of symmetric groups and related graphs
• Distinguishing numbers for graphs and groups
• Distinguishing Numbers and Generalizations
• Asymmetric edge-coloring of graphs with simple automorphism group
• Stabilizing on the distinguishing number of a graph