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Graphs With Stability Index One

Published online by Cambridge University Press:  09 April 2009

D. A. Holton  and
J. A. Sims
D. A. Holton
Affiliation:
Department of Mathematics, University of MelbourneVictoria 3052, Australia.
J. A. Sims
Affiliation:
Linacre College, Oxford University Oxford, England.
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Abstract

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We consider the effect on the stability properties of a graph G, of the presence in the automorphism group of G of automorphisms (uv)h, where u and v are vertices of G, and h is a permutation of vertices of G excluding u and v. We find sufficient conditions for an arbitrary graph and a cartesian product to have stability index one, and conjecture in the latter case that they are necessary. Finally we exhibit explicitly a large class of graphs which have stability index one.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 2 , September 1976 , pp. 212 - 220
Copyright
Copyright © Australian Mathematical Society 1976

References

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