Spectral Turán problem for $t{\mathcal{K}}_4^{-}$-free unbalanced signed graphs

Abstract

Let $t{K}_4$ 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 $t{K}_4$. 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.