Forbidden minors for the class of graphs G with $\xi (G) \leq 2$

L. Hogben, H. Holst, van der

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17 Citations (Scopus)
2 Downloads (Pure)

Abstract

For a given simple graph G, is defined to be the set of real symmetric matrices A whose (i,j)th entry is nonzero whenever i¿j and ij is an edge in G. In [F. Barioli, S. Fallat, L. Hogben, A variant on the graph parameters of Colin de Verdière: Implications to the minimum rank of graphs, Electron. J. Linear Algebra 13 (2005) 387–404.], ¿(G) is defined to be the maximum corank (i.e., nullity) among having the Strong Arnold Property; ¿ is used to study the minimum rank/maximum eigenvalue multiplicity problem for G. Since ¿ is minor monotone, the graphs G such that ¿(G)k can be described by a finite set of forbidden minors. We determine the forbidden minors for ¿(G)2 and present an application of this characterization to computation of minimum rank among matrices in .
Original languageEnglish
Pages (from-to)42-52
JournalLinear Algebra and Its Applications
Volume423
Issue number1
DOIs
Publication statusPublished - 2007

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