A characterization of \((K_n,U^-)\) in the class L(3)

Let \((K_{n},H^-)\) $(K_n,H^{-})$ be a complete sigraph whose negative edges induce a subgraph H. Let L(3) be the class of all sigraphs having exactly three non-negative eigenvalues (including their multiplicities). In this paper, we characterize \((K_n,U^-)\in L(3)\) $(K_n,U^{-})\in L(3)$ , where U is a non-spanning unicyclic subgraph of \( K_n \) $K_n$ .