On some classes of bivalent and trivalent planar graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915292746088448 |
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| author | Alencar, Jorge Caputo, Jean-Guy de Lima, Leonardo Knippel, Arnaud |
| author_facet | Alencar, Jorge Caputo, Jean-Guy de Lima, Leonardo Knippel, Arnaud |
| contents | A graph is called bivalent or trivalent if there exists an eigenvector of the graph Laplacian composed from {-1,1} or {-1,0,1}, respectively. These bivalent and trivalent eigenvectors are important for engineering applications, in particular for vibrating systems. In this article, we determine the structure of bivalent and trivalent graphs in the following planar graph families: trees, unicyclic, bicyclic, and cactus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13199 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On some classes of bivalent and trivalent planar graphs Alencar, Jorge Caputo, Jean-Guy de Lima, Leonardo Knippel, Arnaud Combinatorics Mathematical Physics Spectral Theory A graph is called bivalent or trivalent if there exists an eigenvector of the graph Laplacian composed from {-1,1} or {-1,0,1}, respectively. These bivalent and trivalent eigenvectors are important for engineering applications, in particular for vibrating systems. In this article, we determine the structure of bivalent and trivalent graphs in the following planar graph families: trees, unicyclic, bicyclic, and cactus. |
| title | On some classes of bivalent and trivalent planar graphs |
| topic | Combinatorics Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2505.13199 |