## Abstract

The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real

matrices whose ijth entry (for i /= j ) is nonzero whenever {i, j } is an edge in G and is zero otherwise. This

paper introduces a new graph parameter, Z(G), that is the minimum size of a zero forcing set of vertices

and uses it to bound the minimum rank for numerous families of graphs, often enabling computation of the

minimum rank.

matrices whose ijth entry (for i /= j ) is nonzero whenever {i, j } is an edge in G and is zero otherwise. This

paper introduces a new graph parameter, Z(G), that is the minimum size of a zero forcing set of vertices

and uses it to bound the minimum rank for numerous families of graphs, often enabling computation of the

minimum rank.

Original language | English |
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Pages (from-to) | 1628-1648 |

Journal | Linear Algebra and its Applications |

Volume | 428 |

Issue number | 7 |

Publication status | Published - 2008 |

## Keywords

- minimum rank
- rank
- graph
- symmetric matrix
- matrix