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Linear Algebra and its Applications 421 (2007) 252263 www.elsevier.com/locate/laa
 

Summary: Linear Algebra and its Applications 421 (2007) 252263
www.elsevier.com/locate/laa
On the minimum rank of the join of graphs
and decomposable graphs
Francesco Barioli a, Shaun Fallat b,,,1
a Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403-2504, USA
b Department of Mathematics and Statistics, University of Regina, Regina, SK, Canada S4S 0A2
Received 22 November 2005; accepted 22 May 2006
Available online 10 August 2006
Submitted by L. Hogben
Abstract
For a given undirected graph G, the minimum rank of G is defined to be the smallest possible rank over
all real symmetric matrices A whose (i, j)th entry is nonzero whenever i /= j and {i, j} is an edge in G.
In this work we consider joins and unions of graphs, and characterize the minimum rank of such graphs in
the case of `balanced inertia'. Several consequences are provided for decomposable graphs, also known as
cographs.
2006 Elsevier Inc. All rights reserved.
AMS classification: 05C50; 15A03; 15A18
Keywords: Graphs; Minimum rank; Maximum multiplicity; Decomposable graphs; Join; Union; Inertia-balanced;
Cographs

  

Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina

 

Collections: Mathematics