Determining the maximal degree of a tree given by its distance matrix
The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order which corresponds to the transposition of a pair of elements in a permutation. We introduce an extension of this partial order, which we call the stochastic Bruhat order, for the larger class of doubly stochastic matrices (convex hull of permutation matrices). An alternative description of this partial order is given. We define a class of special faces of induced by permutation matrices,...
We obtain upper bounds for generalized indices of matrices in the class of nearly reducible Boolean matrices and in the class of critically reducible Boolean matrices, and prove that these bounds are the best possible.