Abstract
These lectures introduce the finite graph theorist to a medley of topics and theorems in infinite graphs theory. Section 1: three graph theoretical notions required for a study of infinite graphs, namely end-equivalence (as developed by R. Halin), a refinement of the notion of connectivity, and growth. Section 2: an extension to infinite graphs (by C. Thomassen and the author) of W.T. Tutte’s thoerem on arc-transitivity. Section 3: twoended graphs, especially various characterizations of strips. Section 4: rays, double rays, quasi-axes, and the automorphism group action upon them. Section 5: joint work by P. Niemeyer and the author on fiber-equivalence, which is a refinement of end-equivalence. Section 6: the classification of locally finite, edge-transitive planar graphs by J.E. Graver and the author in terms of the number of ends, their Petrie walks, and the local behavior of their automorphism groups.
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Watkins, M.E. (1997). Ends and automorphisms of infinite graphs. In: Hahn, G., Sabidussi, G. (eds) Graph Symmetry. NATO ASI Series, vol 497. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8937-6_9
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DOI: https://doi.org/10.1007/978-94-015-8937-6_9
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