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- Title
On k-geodetic graphs and groups.
- Authors
Elder, Murray; Piggott, Adam; Townsend, Kane
- Abstract
We call a graph k-geodetic, for some k ≥ 1 , if it is connected and between any two vertices there are at most k geodesics. It is shown that any hyperbolic group with a k-geodetic Cayley graph is virtually-free. Furthermore, in such a group the centralizer of any infinite order element is an infinite cyclic group. These results were known previously only in the case that k = 1. A key tool used to develop the theorem is a new graph theoretic result concerning "ladder-like structures" in a k-geodetic graph.
- Subjects
HYPERBOLIC groups; INFINITE groups; CYCLIC groups; CAYLEY graphs; GEODESICS
- Publication
International Journal of Algebra & Computation, 2023, Vol 33, Issue 6, p1169
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196723500534