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Let $\mathcal{C}_{k}^{-}$ be the set of all negative $C_k$. For odd cycle,Wang, Hou and Li [29] gave a spectral condition for the existence of negative$C_3$ in unbalanced signed graphs. For even cycle, we determine the maximumindex among all $\mathcal{C}_4^{-}$-free unbalanced signed graphs andcompletely characterize the extremal signed graph in this paper. This could beregarded as a signed graph version of the results by Nikiforov [23] and Zhaiand Wang [37].

The largest eigenvalue of $\mathcal{C}_4^{-}$-free signed graphs