On Graphs with Given Automorphism Group

P. J. Cameron

doi:10.1016/S0195-6698(80)80043-6

On Graphs with Given Automorphism Group

P. J. Cameron^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	91-96
Number of pages	6
Journal	European Journal of Combinatorics
Volume	1
Issue number	2
DOIs	https://doi.org/10.1016/S0195-6698(80)80043-6
Publication status	Published - 1 Jan 1980

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On Graphs with Given Automorphism Group

Abstract

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