Signed Complete Graphs with Negative Paths

Let I = (G,o) be a signed graph, where G is the underlying simple graph and o : E(G) {-, +} is the sign function on the edges of G. The adjacency matrix of a signed graph has – 1 or +1 for adjacent vertices, depending on the sign of the connecting edges. Let T = (Knum, P) be a signed complete graph whose negative edges induce a subgraph which is the disjoint unio‎n of m distinct paths. In this paper, by a constructive method, we obtain n-1+ 1 (L eigenvalues of T, where [x] denotes the largest integer less than or equal to x.