 
Summary: Linear Algebra and its Applications 429 (2008) 16291638
Available online at www.sciencedirect.com
www.elsevier.com/locate/laa
An upper bound for the minimum rank of a graph
Avi Berman a, Shmuel Friedland b, Leslie Hogben c,d,
,
Uriel G. Rothblum e, Bryan Shader f
a Faculty of Mathematics, Technion, Haifa 32000, Israel
b Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago,
IL 606077045, USA
c Department of Mathematics, Iowa State University, Ames, IA 50011, USA
d American Institute of Mathematics, 360 Portage Avenue, Palo Alto, CA 94306, USA
e Faculty of Industrial Engineering and Management, Technion, Haifa 32000, Israel
f Department of Mathematics, University of Wyoming, Laramie, WY 82071, USA
Received 27 August 2007; accepted 25 April 2008
Available online 16 June 2008
Submitted by Kirkland
Abstract
For a graph G of order n, the minimum rank of G is defined to be the smallest possible rank over all real
symmetric n × n matrices A whose (i, j)th entry (for i /= j) is nonzero whenever {i, j} is an edge in G and
