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Keywords:
generalized ultrametric matrix; $ \mathcal U$ matrix; weighted graph; inverse $M$-matrix
generalized ultrametric matrix; $ \mathcal U$ matrix; weighted graph; inverse $M$-matrix
Summary:
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.
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