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Homogeneous graphs and stability

Published online by Cambridge University Press:  09 April 2009

A. Gardiner
A. Gardiner
Affiliation:
Pure Mathematics, University of Birmingham, Birmingham B15 2TT, England.
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Abstract

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Let Γ be a graph with finite vertex set V. Γ is homogeneous if whenever U1, U2 ⊆ V are such that the vertex subgraphs (U1), (U2) are isomorphic, then every isomorphism from (U1) to (U2) extends to an automorphism of Γ; homogeneous graphs were studied by Sheehan (1974) and were classified by the author. Γ is locally homogeneous if whenever U ⊆ V, then every automorphism of (U) extends to an automorphism of Γ. We prove that every locally homogeneous graph is homogeneous.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 3 , May 1976 , pp. 371 - 375
Copyright
Copyright © Australian Mathematical Society 1976

References

Gardiner, A. (to appear), ‘Homogeneous graphs’, J. Combinatorial Theory.Google Scholar
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