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Sabidussi-type theorems for stability

Published online by Cambridge University Press:  17 April 2009

Douglas D. Grant ,
D.A. Holton  and
K.L. McAvaney
Douglas D. Grant
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria.
D.A. Holton
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria.
K.L. McAvaney
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria.
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In this note we give details of a method by which we can produce an index-0 graph from any unstable graph and use it to show that given any finite group there exists an index-0 graph whose automorphism group is isomorphic, as an abstract group, to the given group. We proceed to construct two infinite families of connected index-0 graphs with connected complements whose automorphism group contains a transposition. This enables us to produce, for any finite group G, an index-0 graph whose automorphism group, isomorphic as an abstract group to C2 × G, contains a transposition.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 1 , February 1974 , pp. 95 - 105
Copyright
Copyright © Australian Mathematical Society 1974

References

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