Extremal matrices for the Bruhat-graph order

Rosário Fernandes, Susana Furtado

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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Abstract

We consider the class (Formula presented.) of symmetric (Formula presented.) -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 (Formula presented.) the two orders are distinct. In this paper we give general properties of minimal and maximal matrices for these orders on (Formula presented.) and study the minimal and maximal matrices when k = 1, 2 or 3.

Original languageEnglish
Pages (from-to)1255-1274
JournalLinear and Multilinear Algebra
Volume69
Issue number7
DOIs
Publication statusPublished - 19 May 2021

Keywords

  • -Matrices
  • 05B20
  • 06A07
  • Bruhat order
  • maximal matrices
  • minimal matrices
  • symmetric matrices

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