Abstract
We study transitivity properties of graphs with more than one end. We completely classify the distance-transitive such graphs and, for all k≥3, the k-CS-transitive such graphs.
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References
- [1]
W. Dicks, M. J. Dunwoody: Groups Acting on Graphs, Cambridge Stud. Adv. Math., vol. 17, Cambridge Univ. Press, Cambridge, 1989.
- [2]
R. Diestel: Graph Theory, 3rd ed. Springer-Verlag, 2005.
- [3]
M. J. Dunwoody, B. Krön: Vertex cuts, arXiv:0905.0064v3.
- [4]
H. Enomoto: Combinatorially homogeneous graphs, J. Combin. Theory Ser. B 30(2) (1981), 215–223.
- [5]
A. Gardiner: Homogeneous graphs, J. Combin. Theory Ser. B 20(1) (1976), 94–102.
- [6]
R. Gray: k-CS-transitive infinite graphs, J. Combin. Theory Ser. B 99(2) (2009), 378–398.
- [7]
R. Gray, D. Macpherson: Countable connected-homogeneous graphs, J. Combin. Theory Ser. B 100(2) (2010), 97–118.
- [8]
A. A. Ivanov: Bounding the diameter of a distance-regular graph, Dokl. Akad. Nauk SSSR 271(4) (1983) 789–792.
- [9]
B. Krön: End compactifications in non-locally-finite graphs, Math. Proc. Camb. Phil. Soc. 131(3) (2001), 427–443.
- [10]
B. Krön, R. G. Möller: Metric ends, fibers and automorphisms of graphs, Math. Nachr. 281(1) (2008), 62–74.
- [11]
H. D. Macpherson: Infinite distance transitive graphs of finite valency, Combinatorica 2(1) (1982), 63–69.
- [12]
R. G. Möller: Accessibility and ends of graphs, J. Combin. Theory Ser. B 66(2) (1996), 303–309.
- [13]
R. G. Möller: Distance-transitivity in infinite graphs, J. Combin. Theory Ser. B 60(1) (1994), 36–39.
- [14]
R. G. Möller: Groups acting on locally finite graphs-a survey of the infinitely ended case, In: Groups’ 93 Galway/St. Andrews, Vol. 2, 426–456. Cambridge Univ. Press, Cambridge, 1995.
- [15]
C. Ronse: On homogenous graphs, J. London Math. Soc. (2) 17(3) (1978), 375–379.
- [16]
C. Thomassen, W. Woess: Vertex-transitive graphs and accessibility, J. Combin. Theory Ser. B 58(2) (1993), 248–268.
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Hamann, M., Pott, J. Transitivity conditions in infinite graphs. Combinatorica 32, 649–688 (2012). https://doi.org/10.1007/s00493-012-2694-z
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Mathematics Subject Classification (2010)
- 05C25
- 05C63