Convex combination of first and second eigenvalues of trees
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918290231656448 |
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| author | Kumar, Hitesh Mohar, Bojan Pragada, Shivaramakrishna Zhan, Hanmeng |
| author_facet | Kumar, Hitesh Mohar, Bojan Pragada, Shivaramakrishna Zhan, Hanmeng |
| contents | For a graph $G$, let $λ_1(G)$ and $λ_2(G)$ denote the largest and the second largest adjacency eigenvalue of $G$. The sum $λ_1(G) + λ_2(G)$ is called the \emph{spectral sum} of $G$. We investigate the spectral sum of trees of order $n$ and determine the extremal trees that achieve maximum/minimum. Moreover, for any $α\in [0,1]$, we determine the extremal trees which maximize the convex combination $αλ_1 + (1-α)λ_2$ in the class of $n$-vertex trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10036 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convex combination of first and second eigenvalues of trees Kumar, Hitesh Mohar, Bojan Pragada, Shivaramakrishna Zhan, Hanmeng Combinatorics 05C50, 05C05 For a graph $G$, let $λ_1(G)$ and $λ_2(G)$ denote the largest and the second largest adjacency eigenvalue of $G$. The sum $λ_1(G) + λ_2(G)$ is called the \emph{spectral sum} of $G$. We investigate the spectral sum of trees of order $n$ and determine the extremal trees that achieve maximum/minimum. Moreover, for any $α\in [0,1]$, we determine the extremal trees which maximize the convex combination $αλ_1 + (1-α)λ_2$ in the class of $n$-vertex trees. |
| title | Convex combination of first and second eigenvalues of trees |
| topic | Combinatorics 05C50, 05C05 |
| url | https://arxiv.org/abs/2601.10036 |