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Ends of graphs

Published online by Cambridge University Press:  24 October 2008

Rgnvaldur G. Mller
Affiliation:
Mathematical Institute, 2429 St Giles', Oxford OX1 3LB

Abstract

It is shown how questions about ends of locally finite graphs can be reduced to questions about trees. Several applications are given; for example, locally finite connected graphs with infinitely many ends and automorphism groups that act transitively on the ends are classified.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

1Adeleke, S. A. and Neumann, P. M.. Semilinearly ordered sets, betweenness relations and their automorphism groups. In preparation.Google Scholar
2Dicks, W. and Dunwoody, M. J.. Groups Acting on Graphs (Cambridge University Press, 1989).Google Scholar
3Dunwoody, M. J.. Cutting up graphs. Combinatorica 2 (1982), 1523.CrossRefGoogle Scholar
4Godsil, C. D., Imrich, W., Seifter, N., Watkins, M. E. and Woess, W.. A note on bounded automorphisms of infinite graphs. Graphs Combin. 5 (1989), 333338.CrossRefGoogle Scholar
5Halin, R.. ber die Maximalzahl fremder unendlicher Wege in Graphen. Math. Nachr. 30 (1965), 119127.CrossRefGoogle Scholar
6Halin, R.. Automorphisms and endomorphisms of infinite locally finite graphs. Abh. Math. Sent. Univ. Hamburg 39 (1973), 251283.CrossRefGoogle Scholar
7Jung, H. A.. A note on fragments of infinite graphs. Combinatorica 1 (1981), 285288.CrossRefGoogle Scholar
8Macpherson, H. D.. Infinite distance transitive graphs of finite valency. Combinatorica 2 (1982), 6369.CrossRefGoogle Scholar
9Nebbia, C.. Groups of isometries of a tree and the KunzeStein phenomenon. Pacific J. Math. 133 (1988), 141149.CrossRefGoogle Scholar
10Nebbia, C.. Amenability and KunzeStein property for groups acting on a tree. Pacific J. Math. 135 (1988), 371380.CrossRefGoogle Scholar
11Soardi, P. M. and Woess, W.. Amenability, unimodularity, and the spectral radius of random walks on infinite graphs. Math. Z. 205 (1990), 471486.CrossRefGoogle Scholar
12Tits, J.. Sur le groupe des automorphismes d'un arbre. In Essays on Topology and Related Topics. (Mmoires ddis a G. de Rham) (Springer-Verlag, 1970), pp. 188211.CrossRefGoogle Scholar
13Woess, W.. Amenable group actions on infinite graphs. Math. Ann. 284 (1989), 251265.CrossRefGoogle Scholar
14Woess, W.. Boundaries of random walks on graphs and groups with infinitely many ends. Israel J. Math. 68 (1989), 271301.CrossRefGoogle Scholar
15Woess, W.. Topological groups and infinite graphs. Ann. Discrete Math., to appear.Google Scholar