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

DOI10.1016/j.laa.2006.08.003zbMath1118.05064OpenAlexW1974791842MaRDI QIDQ876301

Leslie Hogben, Hein van der Holst

Publication date: 18 April 2007

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

Full work available at URL: https://doi.org/10.1016/j.laa.2006.08.003

zbMATH Keywords

Symmetric matrixCorankGraph minorMinimum rankStrong Arnold property

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Graph minors (05C83) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (17)

Using a new zero forcing process to guarantee the strong Arnold property ⋮ The inertia set of a signed graph ⋮ Computational and Theoretical Challenges for Computing the Minimum Rank of a Graph ⋮ On the Wiener index, distance cospectrality and transmission-regular graphs ⋮ Some bounds on the zero forcing number of a graph ⋮ On the minimum rank of the third power of a starlike tree ⋮ Orthogonal representations, minimum rank, and graph complements ⋮ Three-connected graphs whose maximum nullity is at most three ⋮ Two-connected signed graphs with maximum nullity at most two ⋮ The minimum rank of matrices and the equivalence class graph ⋮ Parameters Related to Tree‐Width, Zero Forcing, and Maximum Nullity of a Graph ⋮ Zero forcing sets and the minimum rank of graphs ⋮ Minimum rank of skew-symmetric matrices described by a graph ⋮ Techniques for determining the minimum rank of a small graph ⋮ Signed graphs with stable maximum nullity at most two ⋮ Unnamed Item ⋮ The minimum rank of symmetric matrices described by a graph: a survey

Cites Work

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• Multiplicities of eigenvalues and tree-width of graphs
• Computation of minimal rank and path cover number for certain graphs
• Graphs whose minimal rank is two
• A variant on the graph parameters of Colin de Verdiere: Implications to the minimum rank of graphs

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