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

L. Hogben, H. Holst, van der

17 Citations (Scopus)

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 language English 42-52 Linear Algebra and Its Applications 423 1 https://doi.org/10.1016/j.laa.2006.08.003 Published - 2007

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Forbidden Minor
Minimum Rank
Linear algebra
Graph in graph theory
Nullity
Simple Graph
Symmetric matrix
Electrons
Finite Set
Minor
Monotone
Multiplicity
Electron
Eigenvalue
Class

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Hogben, L. ; Holst, van der, H. / Forbidden minors for the class of graphs G with $\xi (G) \leq 2$. In: Linear Algebra and Its Applications. 2007 ; Vol. 423, No. 1. pp. 42-52.
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Forbidden minors for the class of graphs G with $\xi (G) \leq 2$. / Hogben, L.; Holst, van der, H.

In: Linear Algebra and Its Applications, Vol. 423, No. 1, 2007, p. 42-52.

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