Geodesic
A note on ultrametric matrices
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 4, pp. 929-940.

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It is proved in this paper that special generalized ultrametric and special $\mathcal U$ matrices are, in a sense, extremal matrices in the boundary of the set of generalized ultrametric and $ \mathcal U$ matrices, respectively. Moreover, we present a new class of inverse $M$-matrices which generalizes the class of $\mathcal U$ matrices.
Classification : 05C50, 15A09, 15A48, 15A57
Keywords: generalized ultrametric matrix; $ \mathcal U$ matrix; weighted graph; inverse $M$-matrix 
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     author = {Zhang, Xiao-Dong},
     title = {A note on ultrametric matrices},
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     pages = {929--940},
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     zbl = {1080.15500},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2004__54_4_a8/}
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Zhang, Xiao-Dong. A note on ultrametric matrices. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 4, pp. 929-940. http://geodesic.mathdoc.fr/item/CMJ_2004__54_4_a8/