### Abstract

*A*with a fixed rank

*r*is considered, provided A has no repeated rows or columns. When A is the adjacency matrix of a graph, Kotlov and Lovász [A. Kotlov and L. Lovász. The rank and size of graphs. J. Graph Theory, 23:185–189,

1996.] proved that the maximum order equals Θ

^{(2r/2)}. In this note, it is showed that this result remains correct if

*A*is symmetric, but becomes false if symmetry is not required.

Original language | English |
---|---|

Pages (from-to) | 3-6 |

Journal | Electronic Journal of Linear Algebra |

Volume | 24 |

Publication status | Published - 2012 |

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**The maximum order of reduced square (0,1)-matrices with a given rank.** / Haemers, W.H.; Peeters, M.J.P.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - The maximum order of reduced square (0,1)-matrices with a given rank

AU - Haemers, W.H.

AU - Peeters, M.J.P.

N1 - Appeared earlier as CentER Discussion Paper 2011-113

PY - 2012

Y1 - 2012

N2 - The maximum order of a square (0, 1)-matrix A with a fixed rank r is considered, provided A has no repeated rows or columns. When A is the adjacency matrix of a graph, Kotlov and Lovász [A. Kotlov and L. Lovász. The rank and size of graphs. J. Graph Theory, 23:185–189,1996.] proved that the maximum order equals Θ(2r/2). In this note, it is showed that this result remains correct if A is symmetric, but becomes false if symmetry is not required.

AB - The maximum order of a square (0, 1)-matrix A with a fixed rank r is considered, provided A has no repeated rows or columns. When A is the adjacency matrix of a graph, Kotlov and Lovász [A. Kotlov and L. Lovász. The rank and size of graphs. J. Graph Theory, 23:185–189,1996.] proved that the maximum order equals Θ(2r/2). In this note, it is showed that this result remains correct if A is symmetric, but becomes false if symmetry is not required.

M3 - Article

VL - 24

SP - 3

EP - 6

JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

SN - 1081-3810

ER -