signed complete graphs with negative paths

Let $gamma=(g,sigma)$ be a signed graph, where $g$ is the underlying simple graph and $sigma : e(g) longrightarrow lbrace -,+rbrace$ 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 $gamma=(k_{n},bigcup_{i=1}^{m}p_{r_i}^- )$ 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+sigma _{i=1}^{m}big(lfloor frac{r_i}{2}rfloor-r_ibig) $ eigenvalues of $gamma$, where $lfloor xrfloor$ denotes the largest integer less than or equal to $x$.