P-matrices and signed digraphs

Journal article

Banaji, M and Rutherford, CG (2010). P-matrices and signed digraphs. Discrete Mathematics. 311 (4), pp. 295-301. https://doi.org/10.1016/j.disc.2010.10.018
AuthorsBanaji, M and Rutherford, CG

We associate a signed digraph with a list of matrices whose dimensions permit them to be multiplied, and whose product is square. Cycles in this graph have a parity, that is, they are either even (termed e-cycles) or odd (termed o-cycles). The absence of e-cycles in the graph is shown to imply that the matrix product is a P0-matrix, i.e., all of its principal minors are nonnegative. Conversely, the presence of an e-cycle is shown to imply that there exists a list of matrices associated with the graph whose product fails to be a P0-matrix. The results generalise a number of previous results relating P- and P0-matrices to graphs.

JournalDiscrete Mathematics
Journal citation311 (4), pp. 295-301
Digital Object Identifier (DOI)https://doi.org/10.1016/j.disc.2010.10.018
Publication dates
Print18 Nov 2010
Publication process dates
Deposited19 Dec 2017
Accepted22 Oct 2010
Accepted author manuscript
File Access Level
Permalink -


Download files

Accepted author manuscript
License: CC BY-NC-ND 4.0
File access level: Open

  • 71
    total views
  • 96
    total downloads
  • 2
    views this month
  • 0
    downloads this month

Export as

Related outputs

Generalized pentagonal geometries
Forbes, A. and Rutherford, C. G. (2021). Generalized pentagonal geometries. Journal of Combinatorial Designs. https://doi.org/10.1002/jcd.21811
Some results on the structure and spectra of matrix-products
Banaji, M. and Rutherford, C. G. (2015). Some results on the structure and spectra of matrix-products. Linear Algebra and Its Applications. 474, pp. 192-212. https://doi.org/10.1016/j.laa.2015.02.008
Pancyclicity when each cycle must pass exactly k Hamilton cycle chords.
Chaouche, FA, Rutherford, CG and Whitty, R (2015). Pancyclicity when each cycle must pass exactly k Hamilton cycle chords. Discussiones Mathematicae Graph Theory. 35 (3), pp. 533-539. https://doi.org/10.7151/dmgt.1818
Objective functions with redundant domains
Affif Chaouche, F., Rutherford, C. and Whitty, R. (2012). Objective functions with redundant domains. Journal of Combinatorial Optimization. 26, pp. 372-384. https://doi.org/10.1007/s10878-012-9468-9
Covering radii are not matroid invariants
Britz, T. and Rutherford, C. (2005). Covering radii are not matroid invariants. 296 (1), pp. 117-120. https://doi.org/10.1016/j.disc.2005.03.002