Infinite Planar Graphs

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.

Grantor dc:publisher

University of North Texas

Year dc:date

2000

Author dc:creator

• Aurand, Eric William

Contributors dc:contributor

• Brand, Neal
• Kung, Joseph
• Monticino, Michael G.

• Graph theory.
• Geodesics (Mathematics)
• Automorphisms.
• equivalence classes
• excess of a vertex
• planar graph
• geodesic ray
• automorphism

Statement dc:rights

• Public
• Copyright
• Aurand, Eric William
• Copyright is held by the author, unless otherwise noted. All rights reserved.

Language dc:language

English

Identifier

oclc: 47144615
untcat: b2300272
https://digital.library.unt.edu/ark:/67531/metadc2545/
ark: ark:/67531/metadc2545

OAI identifier oai:identifier

info:ark/67531/metadc2545