The index of $t\mathcal{C}_{3}^{-}$-free signed graphs
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918238011523072 |
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| author | Li, Dan Qin, Mingsong |
| author_facet | Li, Dan Qin, Mingsong |
| contents | The classical spectral Turán problem is to determine the maximum spectral radius of an $F$-free graph of order $n$. This paper extends this framework to signed graphs. Let $\mathcal{C}_r^-$ be the set of all unbalanced signed graphs with underlying graphs $C_r$. Wang, Hou and Li [Linear Algebra Appl, 681 (2024) 47-65] previously determined the spectral Turán number of $\mathcal{C}_{3}^{-}$. In the present work, we characterize the extremal graphs that achieve the maximum index among all unbalanced signed graphs of order $n$ that are $t\mathcal{C}{3}^{-}$-free for $t\geq 2$. Furthermore, for $t\geq 3$, we identify the graphs with the second maximum index among all $t\mathcal{C}{3}^{-}$-free unbalanced signed graphs of fixed order $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The index of $t\mathcal{C}_{3}^{-}$-free signed graphs Li, Dan Qin, Mingsong Combinatorics The classical spectral Turán problem is to determine the maximum spectral radius of an $F$-free graph of order $n$. This paper extends this framework to signed graphs. Let $\mathcal{C}_r^-$ be the set of all unbalanced signed graphs with underlying graphs $C_r$. Wang, Hou and Li [Linear Algebra Appl, 681 (2024) 47-65] previously determined the spectral Turán number of $\mathcal{C}_{3}^{-}$. In the present work, we characterize the extremal graphs that achieve the maximum index among all unbalanced signed graphs of order $n$ that are $t\mathcal{C}{3}^{-}$-free for $t\geq 2$. Furthermore, for $t\geq 3$, we identify the graphs with the second maximum index among all $t\mathcal{C}{3}^{-}$-free unbalanced signed graphs of fixed order $n$. |
| title | The index of $t\mathcal{C}_{3}^{-}$-free signed graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.07579 |