Infinite Planar Graphs

Description:

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.

Creator(s): Aurand, Eric William
Creation Date: May 2000
Partner(s):
UNT Libraries
Collection(s):
UNT Theses and Dissertations
Usage:
Total Uses: 117
Past 30 days: 5
Yesterday: 0
Creator (Author):
Publisher Info:
Publisher Name: University of North Texas
Place of Publication: Denton, Texas
Date(s):
  • Creation: May 2000
  • Digitized: June 26, 2007
Description:

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.

Degree:
Level: Doctoral
Discipline: Mathematics
Language(s):
Subject(s):
Keyword(s): graph | geodesic ray | automorphism
Contributor(s):
Partner:
UNT Libraries
Collection:
UNT Theses and Dissertations
Identifier:
  • OCLC: 47144615 |
  • UNTCAT: b2300272 |
  • ARK: ark:/67531/metadc2545
Resource Type: Thesis or Dissertation
Format: Text
Rights:
Access: Public
License: Copyright
Holder: Aurand, Eric William
Statement: Copyright is held by the author, unless otherwise noted. All rights reserved.