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

Abstract

Let \((K_{n},H^-)\) 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 \((K_n,U^-)\in L(3)\), where U is a non-spanning unicyclic subgraph of \( K_n \).