On the maximum multiplicity of an eigenvalue in a matrix whose graph contains exactly one cycle (Q869912)
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scientific article; zbMATH DE number 5132609
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the maximum multiplicity of an eigenvalue in a matrix whose graph contains exactly one cycle |
scientific article; zbMATH DE number 5132609 |
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On the maximum multiplicity of an eigenvalue in a matrix whose graph contains exactly one cycle (English)
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9 March 2007
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\textit{C. R. Johnson} and \textit{A. L. Duarte} [Linear Multilinear Algebra 46, No. 1--2, 139--144 (1999; Zbl 0929.15005)] proved that for trees \(G\) the maximum possible multiplicity \(M(G)\) of an eigenvalue of a Hermitian matrix whose graph is \(G\) equals the path-covering number of \(G\). The present paper establishes analogous results for some cases of matrices \(G\) whose graph contains exactly one cycle, relating \(M(G)\) to certain parameters associated with \(G\).
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eigenvalues
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Hermitian matrices
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