A note on an infinite family of graphs with all different integral Laplacian eigenvalues
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910586082689024 |
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| author | Dalfó, C. Fiol, M. A. |
| author_facet | Dalfó, C. Fiol, M. A. |
| contents | In this note, we give an infinite family of optimal graphs called $G^+(d,c)$. They are optimal in the sense that they have the maximum possible number of vertices for given a diameter $d$ and the so-called `outer multiset dimension' $c$. We provide their spectra, which have the property that their Laplacian eigenvalues are all different and integral. Finally, we also obtained their eigenvectors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00516 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on an infinite family of graphs with all different integral Laplacian eigenvalues Dalfó, C. Fiol, M. A. Combinatorics In this note, we give an infinite family of optimal graphs called $G^+(d,c)$. They are optimal in the sense that they have the maximum possible number of vertices for given a diameter $d$ and the so-called `outer multiset dimension' $c$. We provide their spectra, which have the property that their Laplacian eigenvalues are all different and integral. Finally, we also obtained their eigenvectors. |
| title | A note on an infinite family of graphs with all different integral Laplacian eigenvalues |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.00516 |