  Let $\Gamma=(G,\sigma)$ be a signed graph, where $\sigma$ is the sign
function on the edges of $G$. In this paper, we use the operation of partial
transpose to obtain non-isomorphic Laplacian cospectral signed graphs. We will
introduce two new operations on signed graphs. These operations will establish
a relationship between the adjacency spectrum of one signed graph with the
Laplacian spectrum of another signed graph. As an application, these new
operations will be utilized to construct several pairs of cospectral
non-isomorphic signed graphs. Finally, we construct integral signed graphs.
