Spectral Tur\'{a}n problem for $\mathcal{K}_{2,t}^-$-free unbalanced signed graphs

Abstract

We determine the maximum index and the signed graphs with the maximum index among all $\mathcal{K}_{2,t}^-$-free unbalanced signed graphs with fixed order for $t\geq 3$, as well as the second maximum index and the signed graphs with the second maximum index among all $\mathcal{K}_{2,t}^-$-free unbalanced signed graphs with fixed order for $t\geq 4$.