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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Infinite vertex-transitive, edge-transitive non-$ 1$-transitive graphs


Authors: Carsten Thomassen and Mark E. Watkins
Journal: Proc. Amer. Math. Soc. 105 (1989), 258-261
MSC: Primary 05C25
DOI: https://doi.org/10.1090/S0002-9939-1989-0973847-6
MathSciNet review: 973847
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Abstract: We show that every vertex-transitive, edge-transitive graph of odd valence and subexponential growth is $ 1$-transitive, thus extending to infinite graphs a theorem of W. T. Tutte for finite graphs. We describe a number of counterexamples in the case of exponential growth.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0973847-6
Article copyright: © Copyright 1989 American Mathematical Society