Trees and acyclic matrices over arbitrary fields

DOI10.1080/03081087.2015.1045822zbMath1333.05077OpenAlexW1527079481MaRDI QIDQ2787609

Ali Mohammadian

Publication date: 4 March 2016

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

Full work available at URL: https://doi.org/10.1080/03081087.2015.1045822

zbMATH Keywords

treematchingnullityeigenvalue multiplicityacyclic matrix

Mathematics Subject Classification ID

Trees (05C05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (4)

Further generalization of symmetric multiplicity theory to the geometric case over a field ⋮ The number of P-vertices for acyclic matrices with given nullity ⋮ Odd covers of graphs ⋮ The maximum number of Parter vertices of acyclic matrices

Cites Work

• A short proof of the Berge-Tutte formula and the Gallai-Edmonds structure theorem
• The symmetrization of matrices by diagonal matrices
• Spectral multiplicity and splitting results for a class of qualitative matrices
• On multiple eigenvalues of trees
• The second largest eigenvalue of a tree
• Null space structure of tree-patterned matrices
• Minimum rank of a graph over an arbitrary field
• The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree
• The Parter--Wiener Theorem: Refinement and Generalization
• Hermitian Matrices, Eigenvalue Multiplicities, and Eigenvector Components
• A note on the multiplicities of the eigenvalues of a graph
• On the Eigenvalues and Eigenvectors of a Class of Matrices

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