Three-connected graphs whose maximum nullity is at most three

DOI10.1016/j.laa.2008.03.018zbMath1145.05037OpenAlexW2166146423MaRDI QIDQ929488

Hein van der Holst

Publication date: 17 June 2008

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2008.03.018

zbMATH Keywords

graph minorsymmetric matrixtree widthminimum rankstrong Arnold propertynullity 3partial tree

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Graph minors (05C83) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (14)

Maximum generic nullity of a graph ⋮ Maximum nullity of outerplanar graphs and the path cover number ⋮ Techniques for determining equality of the maximum nullity and the zero forcing number of a graph ⋮ On the Wiener index, distance cospectrality and transmission-regular graphs ⋮ On the graph complement conjecture for minimum rank ⋮ Computing inertia sets using atoms ⋮ The minimum semidefinite rank of the complement of partial \(k\)-trees ⋮ Unnamed Item ⋮ Parameters Related to Tree‐Width, Zero Forcing, and Maximum Nullity of a Graph ⋮ The extremal function and Colin de Verdière graph parameter ⋮ Zero forcing sets and the minimum rank of graphs ⋮ On minimum rank and zero forcing sets of a graph ⋮ Expected values of parameters associated with the minimum rank of a graph ⋮ Lower bounds in minimum rank problems

Cites Work

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• Forbidden minors characterization of partial 3-trees
• Multiplicities of eigenvalues and tree-width of graphs
• A correction: Orthogonal representations and connectivity of graphs
• Sur un nouvel invariant des graphes et un critère de planarité. (On a new graph invariant and a planarity criterion)
• Orthogonal representations and connectivity of graphs
• A characterization of tridiagonal matrices
• Graphs whose minimal rank is two
• On Linear Recognition of Tree-Width at Most Four
• A variant on the graph parameters of Colin de Verdiere: Implications to the minimum rank of graphs
• A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth

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