Diameter minimal trees

DOI10.1080/03081087.2015.1057097zbMath1338.05160OpenAlexW1606947639MaRDI QIDQ2787616

Charles R. Johnson, Carlos M. Saiago

Publication date: 4 March 2016

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

Full work available at URL: https://doi.org/10.1080/03081087.2015.1057097

zbMATH Keywords

diameterHermitian matrixmultiplicitiesdistinct eigenvaluesbranch duplication

Mathematics Subject Classification ID

Trees (05C05) Extremal problems in graph theory (05C35) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Distance in graphs (05C12)

Related Items (8)

An explicit upper bound on disparity for trees of a given diameter ⋮ Questions, conjectures, and data about multiplicity lists for trees ⋮ Geometric Parter-Wiener, etc. theory ⋮ Change in vertex status after removal of another vertex in the general setting ⋮ The number of distinct eigenvalues for which an index decreases multiplicity ⋮ The minimum number of eigenvalues of multiplicity one in a diagonalizable matrix, over a field, whose graph is a tree ⋮ Diagonalizable matrices whose graph is a tree: the minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments ⋮ Branch duplication in trees: uniqueness of seeds and enumeration of seeds

Cites Work

• Ordered multiplicity lists for eigenvalues of symmetric matrices whose graph is a linear tree
• The structure of matrices with a maximum multiplicity eigenvalue
• Smith normal form and acyclic matrices
• Construction of acyclic matrices from spectral data
• Inverse eigenvalue problems and lists of multiplicities of eigenvalues for matrices whose graph is a tree: The case of generalized stars and double generalized stars.
• Branch duplication for the construction of multiple eigenvalues in an Hermitian matrix whose graph is a tree
• Partial pole assignment for the vibrating system with aerodynamic effect
• The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree
• The Parter--Wiener Theorem: Refinement and Generalization

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