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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2603.10953 |
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| _version_ | 1866910049421492224 |
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| author | Yang, Xiuwen Zhang, Lin-Peng |
| author_facet | Yang, Xiuwen Zhang, Lin-Peng |
| contents | The Laplacian energy of a digraph $G$ is defined as $\sum_{i=1}^n λ_i^2$, where $λ_i$ are the eigenvalues of the Laplacian matrix of $G$. A (di)graph $G$ is said to be $H$-free if it does not contain a copy of the fixed (di)graph $H$ as a sub(di)graph. In this paper, we extend the Turán problems to spectral Turán problems in digraphs: what is the maximal Laplacian energy of an $H$-free digraph of given order? In particular, we determine the maximum Laplacian energy and characterize the extremal digraphs of $\overrightarrow{C_{k+1}}$-free digraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10953 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Extremal Laplacian energy of $\overrightarrow{C_{k+1}}$-free digraphs Yang, Xiuwen Zhang, Lin-Peng Combinatorics The Laplacian energy of a digraph $G$ is defined as $\sum_{i=1}^n λ_i^2$, where $λ_i$ are the eigenvalues of the Laplacian matrix of $G$. A (di)graph $G$ is said to be $H$-free if it does not contain a copy of the fixed (di)graph $H$ as a sub(di)graph. In this paper, we extend the Turán problems to spectral Turán problems in digraphs: what is the maximal Laplacian energy of an $H$-free digraph of given order? In particular, we determine the maximum Laplacian energy and characterize the extremal digraphs of $\overrightarrow{C_{k+1}}$-free digraphs. |
| title | Extremal Laplacian energy of $\overrightarrow{C_{k+1}}$-free digraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.10953 |