Locally Finite, Planar, Edge-Transitive Graphs (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

American Mathematical Society

Softcover

ISBN 10: 0821805568 ISBN 13: 9780821805565

Publisher: American Mathematical Society, 1997

Synopsis

The nine finite, planar, 3-connected, edge-transitive graphs have been known and studied for many centuries. The infinite, locally finite, planar, 3-connected, edge-transitive graphs can be classified according to the number of their ends (the supremum of the number of infinite components when a finite subgraph is deleted).

Prior to this study the 1-ended graphs in this class were identified by Grünbaum and Shephard as 1-skeletons of tessellations of the hyperbolic plane; Watkins characterized the 2-ended members. Any remaining graphs in this class must have uncountably many ends. In this work, infinite-ended members of this class are shown to exist. A more detailed classification scheme in terms of the tupes of Petrie walks in the graphs in this class and the local structure of their automorphism groups
is presented. Explicit constructions ar devised for all of the graphs in most of the classes under this new classification. Also included are partial results toward the complete description of the graphs in the few remaining classes.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1997
• Language: English
• ISBN 10: 0821805568
• ISBN 13: 9780821805565
• Binding: Paperback
• Number of pages: 75