Name
Abstract | ||
|---|---|---|
We investigate vertex-transitive graphs that admit planar embeddings having infinite faces, i.e., faces whose boundary is a double ray. In the case of graphs with connectivity exactly 2, we present examples wherein no face is finite. In particular, the planar embeddings of the Cartesian product of the r-valent tree with K2 are comprehensively studied and enumerated, as are the automorphisms of the resulting maps, and it is shown for r = 3 that no vertex-transitive group of graph automorphisms is extendable to a group of homeomorphisms of the plane. We present all known families of infinite, locally finite, vertex-transitive graphs of connectivity 3 and an infinite family of 4-connected graphs that admit planar embeddings wherein each vertex is incident with an infinite face. © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 257–275, 2003 |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1002/jgt.v42:4 | Journal of Graph Theory |
Keywords | Field | DocType |
cayley graph | Discrete mathematics,Topology,Combinatorics,Chordal graph,Planar straight-line graph,Book embedding,Pathwidth,1-planar graph,Topological graph theory,Universal graph,Planar graph,Mathematics | Journal |
Volume | Issue | ISSN |
42 | 4 | 0364-9024 |
Citations | PageRank | References |
2 | 0.51 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| C. Paul Bonnington | 1 | 100 | 19.95 |
| Mark E. Watkins | 2 | 109 | 32.53 |