 
Summary: Linear Algebra and its Applications 428 (2008) 16281648
Available online at www.sciencedirect.com
www.elsevier.com/locate/laa
Zero forcing sets and the minimum rank of graphs
AIM Minimum Rank Special Graphs Work Group ,1
American Institute of Mathematics 360 Portage Ave. Palo Alto, CA 94306, USA
Received 6 March 2007; accepted 8 October 2007
Available online 26 November 2007
Submitted by R.A. Brualdi
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.
© 2007 Elsevier Inc. All rights reserved.
AMS classification: 05C50; 15A18; 15A03
Keywords: Minimum rank; Rank; Graph; Symmetric matrix; Matrix
The workshop "Spectra of Families of Matrices described by Graphs, Digraphs, and Sign Patterns", was held at the
American Institute of Mathematics, October 2327, 2006. The authors thank AIM and NSF for their support.
