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Dovgoshey, O.; Petrov, E.; Teichert, H.-M.
Journal of fixed point theory and applications, 06/2017, Letnik: 19, Številka: 2Journal Article
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.
