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arXiv · 2610.15383

Maximum index of unbalanced signed graphs without a positive odd cycle

Li Ma·Linfeng Xie·Xiaogang Liu
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Abstract

Let $\mathcal{C}_{r}^+$ be the set of all balanced signed graphs with underlying graphs $C_r$. A signed graph is called $\mathcal{C}_{r}^+$-free if it contains no subgraph isomorphic to any member of $\mathcal{C}_{r}^+$. In this paper, we characterize the extremal graphs that achieve the maximum index among all $\mathcal{C}_{2k+1}^+$-free unbalanced signed graphs of order $n$ when $k\ge 2$ and $n\ge 187k$.

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Li Ma, Linfeng Xie, Xiaogang Liu. 2026-10-11. Maximum index of unbalanced signed graphs without a positive odd cycle. https://arxiv.org/abs/2610.15383

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