The graphs for which the maximum multiplicity of an eigenvalue is two

DOI10.1080/01445340802354580zbMath1225.05167arXivmath/0701562OpenAlexW2069386774MaRDI QIDQ3399125

Raphael Loewy, Paul Smith, Charles R. Johnson

Publication date: 29 September 2009

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

Full work available at URL: https://arxiv.org/abs/math/0701562

zbMATH Keywords

grapheigenvaluepartial 2-treeminimum rank of a graphexceptional partial 2-treelinear partial 2-tree

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (17)

The inverse inertia problem for graphs: Cut vertices, trees, and a counterexample ⋮ Using a new zero forcing process to guarantee the strong Arnold property ⋮ Computational and Theoretical Challenges for Computing the Minimum Rank of a Graph ⋮ The maximum of the minimal multiplicity of eigenvalues of symmetric matrices whose pattern is constrained by a graph ⋮ On the Wiener index, distance cospectrality and transmission-regular graphs ⋮ A technique for computing the zero forcing number of a graph with a cut-vertex ⋮ Signed graphs with maximum nullity two ⋮ The zero forcing polynomial of a graph ⋮ Two-connected signed graphs with maximum nullity at most two ⋮ Parameters Related to Tree‐Width, Zero Forcing, and Maximum Nullity of a Graph ⋮ On the relationships between zero forcing numbers and certain graph coverings ⋮ Signed graphs with stable maximum nullity at most two ⋮ The minimum rank of symmetric matrices described by a graph: a survey ⋮ Connected zero forcing sets and connected propagation time of graphs ⋮ On the minimum rank of a graph over finite fields ⋮ Maximum nullity and zero forcing number on graphs with maximum degree at most three ⋮ On extremal graphs for zero forcing number

Cites Work

• Graphs whose positive semi-definite matrices have nullity at most two
• On Fiedler's characterization of tridiagonal matrices over arbitrary fields
• Computation of minimal rank and path cover number for certain graphs
• A characterization of tridiagonal matrices
• Steiner trees, partial 2–trees, and minimum IFI networks
• The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree

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