Maximum spectral sum of graphs
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915975201292288 |
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| author | Kumar, Hitesh Liu, Lele Monterde, Hermie Pragada, Shivaramakrishna Tait, Michael |
| author_facet | Kumar, Hitesh Liu, Lele Monterde, Hermie Pragada, Shivaramakrishna Tait, Michael |
| contents | For a graph $G$ of order $n$, the spectral sum of $G$ is defined to be the sum $λ_1(G) + λ_2(G)$, where $λ_1(G)$ (resp. $λ_2(G)$) is the largest (resp. second largest) adjacency eigenvalue of $G$. Ebrahimi, Mohar, Nikiforov and Ahmady (2008) conjectured that the spectral sum \[ λ_1(G) + λ_2(G)\le \frac{8}{7}n \] for any graph $G$. We prove this conjecture by combining tools from the theory of graph limits, convex geometry, exterior algebra and convex optimization. The techniques developed are of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00512 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximum spectral sum of graphs Kumar, Hitesh Liu, Lele Monterde, Hermie Pragada, Shivaramakrishna Tait, Michael Combinatorics 05C50, 15A18, 15A60, 52A38, 15A75, 15A39 For a graph $G$ of order $n$, the spectral sum of $G$ is defined to be the sum $λ_1(G) + λ_2(G)$, where $λ_1(G)$ (resp. $λ_2(G)$) is the largest (resp. second largest) adjacency eigenvalue of $G$. Ebrahimi, Mohar, Nikiforov and Ahmady (2008) conjectured that the spectral sum \[ λ_1(G) + λ_2(G)\le \frac{8}{7}n \] for any graph $G$. We prove this conjecture by combining tools from the theory of graph limits, convex geometry, exterior algebra and convex optimization. The techniques developed are of independent interest. |
| title | Maximum spectral sum of graphs |
| topic | Combinatorics 05C50, 15A18, 15A60, 52A38, 15A75, 15A39 |
| url | https://arxiv.org/abs/2604.00512 |