Maximum nullity of outerplanar graphs and the path cover number

DOI10.1016/j.laa.2009.08.033zbMath1201.05061OpenAlexW2151143642MaRDI QIDQ848586

John Sinkovic

Publication date: 4 March 2010

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

Full work available at URL: https://doi.org/10.1016/j.laa.2009.08.033

zbMATH Keywords

graphouterplanarsymmetricminimum rankpath cover numberpartial 2-path

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (6)

Families of graphs with maximum nullity equal to zero forcing number ⋮ Minimum rank of outerplanar graphs ⋮ Vertex and edge spread of zero forcing number, maximum nullity, and minimum rank of a graph ⋮ Signed graphs with maximum nullity two ⋮ Zero forcing parameters and minimum rank problems ⋮ Signed graphs with stable maximum nullity at most two

Cites Work

• Three-connected graphs whose maximum nullity is at most three
• Computation of minimal rank and path cover number for certain graphs
• The maximum corank of graphs with a 2-separation
• A characterization of tridiagonal matrices
• Minimum-rank matrices with prescribed graph
• On the difference between the maximum multiplicity and path cover number for tree-like graphs
• The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree

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