Infinite Planar Graphs

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How many equivalence classes of geodesic rays does a graph contain? How many bounded automorphisms does a planar graph have? Neimayer and Watkins studied these two questions and answered them for a certain class of graphs. Using the concept of excess of a vertex, the class of graphs that Neimayer and Watkins studied are extended to include graphs with positive excess at each vertex. The results of this paper show that there are an uncountable number of geodesic fibers for graphs in this extended class and that for any graph in this extended class the only bounded automorphism is the ... continued below

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Aurand, Eric William May 2000.

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  • Aurand, Eric William

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How many equivalence classes of geodesic rays does a graph contain? How many bounded automorphisms does a planar graph have? Neimayer and Watkins studied these two questions and answered them for a certain class of graphs.
Using the concept of excess of a vertex, the class of graphs that Neimayer and Watkins studied are extended to include graphs with positive excess at each vertex. The results of this paper show that there are an uncountable number of geodesic fibers for graphs in this extended class and that for any graph in this extended class the only bounded automorphism is the identity automorphism.

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  • May 2000

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  • Sept. 24, 2007, 10:17 p.m.

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  • May 6, 2016, 7:01 p.m.

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Aurand, Eric William. Infinite Planar Graphs, dissertation, May 2000; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc2545/: accessed October 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .