On Graphs with Given Automorphism Group

P. J. Cameron*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Given that a large graph admits a group of automorphisms isomorphic to the abstract group G, what is the probability a(G) that G is its full automorphism group? This rational number can be computed from the structure of G. We determine the groups G with a(G) =1, show a(G) = 0 or 1 for all abelian groups G, and observe that the values of a(G) for metabelian groups G are dense in the unit interval.

Original languageEnglish
Pages (from-to)91-96
Number of pages6
JournalEuropean Journal of Combinatorics
Issue number2
Publication statusPublished - 1 Jan 1980


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