Abstract
We consider the class of symmetric -matrices with zero trace and constant row sums k which can be identified with the class of the adjacency matrices of k-regular undirected graphs. In a previous paper, two partial orders, the Bruhat and the Bruhat-graph order, have been introduced in this class. In fact, when k = 1 or k = 2, it was shown that the two orders coincide, while for the two orders are distinct. In this paper we give general properties of minimal and maximal matrices for these orders on and study the minimal and maximal matrices when k = 1, 2 or 3.
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