Extremal graphs for the sum of the first two largest signless Laplacian eigenvalues
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908304238706688 |
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| author | Zhou, Zi-Ming Du, Zhi-Bin He, Chang-Xiang |
| author_facet | Zhou, Zi-Ming Du, Zhi-Bin He, Chang-Xiang |
| contents | For a graph $G$, let $S_2(G)$ be the sum of the first two largest signless Laplacian eigenvalues of $G$, and $f(G)=e(G)+3-S_2(G)$. Very recently, Zhou, He and Shan proved that $K^+_{1,n-1}$ (the star graph with an additional edge) is the unique graph with minimum value of $f(G)$ among graphs on $n$ vertices. In this paper, we prove that $K^+_{1,e(G)-1}$ is the unique graph with minimum value of $f(G)$ among graphs with $e(G)$ edges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04389 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extremal graphs for the sum of the first two largest signless Laplacian eigenvalues Zhou, Zi-Ming Du, Zhi-Bin He, Chang-Xiang Combinatorics For a graph $G$, let $S_2(G)$ be the sum of the first two largest signless Laplacian eigenvalues of $G$, and $f(G)=e(G)+3-S_2(G)$. Very recently, Zhou, He and Shan proved that $K^+_{1,n-1}$ (the star graph with an additional edge) is the unique graph with minimum value of $f(G)$ among graphs on $n$ vertices. In this paper, we prove that $K^+_{1,e(G)-1}$ is the unique graph with minimum value of $f(G)$ among graphs with $e(G)$ edges. |
| title | Extremal graphs for the sum of the first two largest signless Laplacian eigenvalues |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2504.04389 |