Geodesic
On infinite, cubic, vertex-transitive graphs with applications to totally disconnected, locally compact groups
Arnbjörg Soffía Árnadóttir1 ; Waltraud Lederle2 ; Rögnvaldur G. Möller3
1Technical University of Denmark
2UCLouvain
3University of Iceland
The electronic journal of combinatorics, Tome 29 (2022) no. 4
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We study groups acting vertex-transitively and non-discretely on connected, cubic graphs (regular graphs of degree 3). Using ideas from Tutte's fundamental papers in 1947 and 1959, it is shown that if the action is edge-transitive, then the graph has to be a tree. When the action is not edge-transitive Tutte's ideas are still useful and can, amongst other things, be used to fully classify the possible two-ended graphs. Results about cubic graphs are then applied to Willis' scale function from the theory of totally disconnected, locally compact groups. Some of the results in this paper have most likely been known to experts but most of them are not stated explicitly with proofs in the literature.
DOI : 10.37236/10709
Classification : 05E18, 05C63, 20B27, 22D05, 20E08
Mots-clés : cubic graphs, Willis' scale function

Arnbjörg Soffía Árnadóttir  1   ; Waltraud Lederle  2   ; Rögnvaldur G. Möller  3

1 Technical University of Denmark
2 UCLouvain
3 University of Iceland 
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     title = {On infinite, cubic, vertex-transitive graphs with applications to totally disconnected, locally compact groups},
     journal = {The electronic journal of combinatorics},
     year = {2022},
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Arnbjörg Soffía Árnadóttir; Waltraud Lederle; Rögnvaldur G. Möller. On infinite, cubic, vertex-transitive graphs with applications to totally disconnected, locally compact groups. The electronic journal of combinatorics, Tome 29 (2022) no. 4. doi: 10.37236/10709

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