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.
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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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/

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