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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.

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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Yap, H. P. (1974), ‘Some remarks on stable graphs’, Bull. Austral. Math. Soc. 10, 351–357.CrossRefGoogle Scholar