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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.03645 |
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| _version_ | 1866911651775643648 |
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| author | Borg, James L. Sciriha, Irene Sherman, Zoia |
| author_facet | Borg, James L. Sciriha, Irene Sherman, Zoia |
| contents | Threshold graphs are graphs that can be characterized in a number of different ways. For example, they are graphs that are $P_4,\ C_4,\ 2K_2$--free. They may also be characterized by a finite sequence of positive integers $a_1, \ldots, a_r$, such that $a_1\geqslant 2$ and $a_1 + a_2 + \cdots + a_r = |V(G)|$.
Threshold graphs have the remarkable property that all graphs of the same order share a common integer Laplacian eigenbasis. This property characterizes threshold graphs. This result was proved in \cite{MachareteDelVecchio}. We give a different proof of the same result. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_03645 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Note on the Laplacian Eigenvectors of Threshold Graphs Borg, James L. Sciriha, Irene Sherman, Zoia Combinatorics 05C50 Threshold graphs are graphs that can be characterized in a number of different ways. For example, they are graphs that are $P_4,\ C_4,\ 2K_2$--free. They may also be characterized by a finite sequence of positive integers $a_1, \ldots, a_r$, such that $a_1\geqslant 2$ and $a_1 + a_2 + \cdots + a_r = |V(G)|$. Threshold graphs have the remarkable property that all graphs of the same order share a common integer Laplacian eigenbasis. This property characterizes threshold graphs. This result was proved in \cite{MachareteDelVecchio}. We give a different proof of the same result. |
| title | A Note on the Laplacian Eigenvectors of Threshold Graphs |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2605.03645 |