Stability of arc-transitive graphs (Q2757096)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Stability of arc-transitive graphs |
scientific article; zbMATH DE number 1675824
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability of arc-transitive graphs |
scientific article; zbMATH DE number 1675824 |
Statements
Stability of arc-transitive graphs (English)
0 references
14 July 2002
0 references
canonical double cover
0 references
automorphism group
0 references
stable graph
0 references
0 references
0.9330025
0 references
0.93084276
0 references
0 references
0 references
0 references
0.9094671
0 references
0.89903617
0 references
0 references
A graph \(G\) is said to be stable if the automorphism group of the direct product \(G\times K_2\) (that is, the bipartite double of \(G\)) is isomorphic to \(\text{Aut}(G)\times\mathbb{Z}_2\). In the paper it is shown, somewhat contrary to expectations, that instability among arc-transitive graphs is not as rare as previously thought. The author describes several methods for constructing unstable arc-transitive graphs and gives three infinite families of such graphs as applications.
0 references
