Minimal asymmetric graphs

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Abstract

Confirming a conjecture of Nešetřil, we show that up to isomorphism there are only finitely many finite minimal asymmetric undirected graphs. In fact, there are exactly 18 such graphs. We also show that these graphs are exactly the finite minimal involution-free graphs.

Keywords

Asymmetric graphs
Involution-free graphs
Automorphisms
Characterization

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