Let be a signed complete graph of order whose negative edges induce a subgraph . If is a disjoint :union: of two graphs and , then we denote by . Let be the adjacency matrix of . The characteristic polynomial and eigenvalues ofare called the characteristic polynomial and eigenvalues of , respectively. The index of is the largest eigenvalue of . In this paper, we study the characteristic polynomial of where is the disjoint :union: of complete graphs and is an arbitrary subgraph of Also, we compute the characteristic polynomial of for some classes of cactus graphs and provide a sharp bound for the index of .
