Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 973847
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] I. Z. Bouwer, Vertex and edge transitive, but not 1-transitive, graphs, Canad. Math. Bull. 13 (1970), 231–237. MR 0269532
  • [2] R. Halin, Über unendliche Wege in Graphen, Math. Ann. 157 (1964), 125–137 (German). MR 0170340
  • [3] R. Halin, Automorphisms and endomorphisms of infinite locally finite graphs, Abh. Math. Sem. Univ. Hamburg 39 (1973), 251–283. MR 0335368
  • [4] H. A. Jung, A note on fragments of infinite graphs, Combinatorica 1 (1981), no. 3, 285–288. MR 637833, 10.1007/BF02579334
  • [5] W. T. Tutte, Connectivity in graphs, Mathematical Expositions, No. 15, University of Toronto Press, Toronto, Ont.; Oxford University Press, London, 1966. MR 0210617

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05C25

Retrieve articles in all journals with MSC: 05C25

Additional Information

Article copyright: © Copyright 1989 American Mathematical Society