Spectral Tur\'an problem for $t\mathcal{K}_{4}^{-}$-free unbalanced signed graphs

Abstract

Let $tK_4$ denote the family of all graphs consisting of $t$ copies of $K_4$ that are allowed to share vertices and $t\mathcal{K}_{4}^{-}$ be the set of all unbalanced signed graphs whose underlying graphs are elements of $tK_4$. In this paper, we characterize the extremal graphs that achieve the maximum index and spectral radius among all $t\mathcal{K}_{4}^{-}$-free unbalanced signed graphs with given order.