On eigenspaces of some compound signed graphs

In the theory of (simple) graphs the concepts of the line and subdivision graph (as compound graphs) are well-known. It is possible to consider them also in the context of (edge) signed graphs. Some relations between the Laplacian spectrum of signed graphs and adjacency spectra of their associated compound (signed) graphs have been recently established in the literature. In this paper, we study the relations between the corresponding eigenspaces.