Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications
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| Format: | Preprint |
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2026
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| _version_ | 1866917546524934144 |
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| author | Sun, Shaowei Min, Yaping Das, Kinkar Chandra |
| author_facet | Sun, Shaowei Min, Yaping Das, Kinkar Chandra |
| contents | This paper establishes new upper bounds for the sum of the $k$ largest eigenvalues of symmetric matrices. When applied to the adjacency matrix of a graph, our results improve upon a related bound due to Mohar {\bf [On the sum of k largest eigenvalues of graphs and symmetric matrices, J. Combin. Theory Ser. B 99 (2009) 306--313]}. Furthermore, in the case of the Laplacian matrix, we prove that the well-known Brouwer's conjecture {\bf [Spectra of Graphs, Springer, New York, 2012]} holds for small values of $k$ for almost all graphs, thereby taking a significant step toward its complete resolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26707 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Sun, Shaowei Min, Yaping Das, Kinkar Chandra Combinatorics 05C50 This paper establishes new upper bounds for the sum of the $k$ largest eigenvalues of symmetric matrices. When applied to the adjacency matrix of a graph, our results improve upon a related bound due to Mohar {\bf [On the sum of k largest eigenvalues of graphs and symmetric matrices, J. Combin. Theory Ser. B 99 (2009) 306--313]}. Furthermore, in the case of the Laplacian matrix, we prove that the well-known Brouwer's conjecture {\bf [Spectra of Graphs, Springer, New York, 2012]} holds for small values of $k$ for almost all graphs, thereby taking a significant step toward its complete resolution. |
| title | Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2605.26707 |