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In this article we examine the adjacency and Laplacian matrices and theireigenvalues and energies of the general product (non-complete extended $p$-sum,or NEPS) of signed graphs. We express the adjacency matrix of the product interms of the Kronecker matrix product and the eigenvalues and energy of theproduct in terms of those of the factor signed graphs. For the Cartesianproduct we characterize balance and compute expressions for the Laplacianeigenvalues and Laplacian energy. We give exact results for those signedplanar, cylindrical and toroidal grids which are Cartesian products of signedpaths and cycles.  We also treat the eigenvalues and energy of the line graphs of signed graphs,and the Laplacian eigenvalues and Laplacian energy in the regular case, withapplication to the line graphs of signed grids that are Cartesian products andto the line graphs of all-positive and all-negative complete graphs.

On Products and Line Graphs of Signed Graphs, their Eigenvalues and Energy