Forbidden minors for the class of graphs G with ξ(G) ⩽ 2

Date
2007-05-01
Authors
Hogben, Leslie
van der Holst, Hein
Hogben, Leslie
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Mathematics
Organizational Unit
Journal Issue
Series
Department
Mathematics
Abstract

For a given simple graph G, S(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.], ξ(G) is defined to be the maximum corank (i.e., nullity) among A∈S(G) having the Strong Arnold Property; ξ is used to study the minimum rank/maximum eigenvalue multiplicity problem for G. Since ξ is minor monotone, the graphs G such that ξ(G)⩽k can be described by a finite set of forbidden minors. We determine the forbidden minors for ξ(G)⩽2 and present an application of this characterization to computation of minimum rank among matrices in S(G).

Comments

This is a manuscript of an article from Linear Algebra and its Applications 423 (2007): 42, doi:10.1016/j.laa.2006.08.003. Posted with permission.

Description
Keywords
Citation
DOI
Collections