Locally Finite, Planar, Edge-Transitive Graphs PDF Download

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Locally Finite, Planar, Edge-Transitive Graphs

Locally Finite, Planar, Edge-Transitive Graphs PDF Author: Jack E. Graver
Publisher: American Mathematical Soc.
ISBN: 0821805568
Category : Mathematics
Languages : en
Pages : 89

Book Description
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 end. The 1-ended graphs in this class were identified by Grünbaum and Shephard; Watkins characterized the 2-ended members. Any remaining graphs in this class must have uncountably may ends. In this work, infinite-ended members of this class are shown to exist. A more detailed classification scheme in terms of the types of Petrie walks in the graphs in this class and the local structure of their automorphism groups is presented.
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