Classification of borderenergetic chemical graphs and borderenergetic graphs of order 12
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909958733299712 |
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| author | Csikvári, Péter Damnjanović, Ivan Milošević, Marko Stanković, Ivan Stevanović, Dragan |
| author_facet | Csikvári, Péter Damnjanović, Ivan Milošević, Marko Stanković, Ivan Stevanović, Dragan |
| contents | The energy $E(G)$ of a simple graph $G$ is the sum of absolute values of the eigenvalues of its adjacency matrix. A borderenergetic graph of order $n \in \mathbb{N}$ is any noncomplete graph~$G$ such that $E(G) = E(K_n) = 2n - 2$. Here we combine two-phase computer-assisted search with theoretical arguments to show that there are only three borderenergetic chemical graphs, thus completing the earlier findings of Li, Wei and Zhu [MATCH Commun. Math. Comput. Chem. 77 (2017), 25-36]. We perform two-phase computer-assisted search to also find all $566$ borderenergetic graphs of order~$12$, thereby correcting and extending the results from a previous search performed by Furtula and Gutman [Iranian J. Math. Chem. 8(4) (2017), 339-344]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of borderenergetic chemical graphs and borderenergetic graphs of order 12 Csikvári, Péter Damnjanović, Ivan Milošević, Marko Stanković, Ivan Stevanović, Dragan Combinatorics 05C09, 05C92, 05C50 The energy $E(G)$ of a simple graph $G$ is the sum of absolute values of the eigenvalues of its adjacency matrix. A borderenergetic graph of order $n \in \mathbb{N}$ is any noncomplete graph~$G$ such that $E(G) = E(K_n) = 2n - 2$. Here we combine two-phase computer-assisted search with theoretical arguments to show that there are only three borderenergetic chemical graphs, thus completing the earlier findings of Li, Wei and Zhu [MATCH Commun. Math. Comput. Chem. 77 (2017), 25-36]. We perform two-phase computer-assisted search to also find all $566$ borderenergetic graphs of order~$12$, thereby correcting and extending the results from a previous search performed by Furtula and Gutman [Iranian J. Math. Chem. 8(4) (2017), 339-344]. |
| title | Classification of borderenergetic chemical graphs and borderenergetic graphs of order 12 |
| topic | Combinatorics 05C09, 05C92, 05C50 |
| url | https://arxiv.org/abs/2512.11684 |