Special Ultrametric Matrices and Graphs

@article{Fiedler2000SpecialUM,
  title={Special Ultrametric Matrices and Graphs},
  author={Miroslav Fiedler},
  journal={SIAM J. Matrix Analysis Applications},
  year={2000},
  volume={22},
  pages={106-113}
}
Special ultrametric matrices are, in a sense, extremal matrices in the boundary of the set of ultrametric matrices introduced by Mart́ınez, Michon, and San Mart́ın [SIAM J. Matrix Anal. Appl., 15 (1994), pp. 98–106]. We show a simple construction of these matrices, if of order n, from nonnegatively edge-weighted trees on n vertices, or, equivalently, from nonnegatively edge-weighted paths. A general ultrametric matrix is then the sum of a nonnegative diagonal matrix and a special ultrametric… CONTINUE READING

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