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

Interlacing Properties of Eigenvalues of Laplacian and Net-Laplacian Matrix of Signed Graphs