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Topics in Topological Graph Theory by Jonathan L. Gross, Robin J. Wilson, Lowell W. Beineke

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14Infinite graphs and planar maps

MARK E. WATKINS

1. Introduction

2. Ends

3. Automorphisms

4. Connectivities

5. Growth

6. Infinite planar graphs and maps

References

        Topological properties of infinite graphs may be global or local. The number of ends (equivalence classes of rays that cannot be separated by a finite subgraph) and whether a given end contains an infinite set of pairwise disjoint rays describe an infinite graph globally. Automorphisms are of interest in terms of both the cardinalities of their set of orbits as well as the cardinalities of the orbits themselves. The notion of connectivity is refined to consider whether the deletion of a subgraph leaves finite or infinite components. The rate of growth, whether polynomial or ...

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