  This paper explores interlacing inequalities in the Laplacian spectrum of
signed cycles and investigates interlacing relationship between the spectrum of
the net-Laplacian of a signed graph and its subgraph formed by removing a
vertex together with its incident edges. Additionally, an inequality is derived
between the net-Laplacian spectrum of a complete co-regular signed graph
$\Gamma$ and the Laplacian spectrum of the graph obtained by removing any
vertex $v$ from $\Gamma$. Also for a signed graph $\Gamma$, the net-Laplacian
matrix is normalized and an inequality is derived between the spectrum of the
normalized net-Laplacian of a signed graph and its subgraph, formed by
contraction of edge and vertex.
