Abstract
A metric space X is rigid if the isometry group of X is trivial. The finite ultrametric spaces X with |X| ≥ 2 are not rigid since for every such X there is a self-isometry having exactly |X|−2 fixed points. Using the representing trees we characterize the finite ultrametric spaces X for which every self-isometry has at least |X|−2 fixed points. Some other extremal properties of such spaces and related graph theoretical characterizations are also obtained.
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Dovgoshey, O., Petrov, E. & Teichert, HM. How rigid the finite ultrametric spaces can be?. J. Fixed Point Theory Appl. 19, 1083–1102 (2017). https://doi.org/10.1007/s11784-016-0329-5
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DOI: https://doi.org/10.1007/s11784-016-0329-5