On the polynomial reconstruction of graphs whose vertex-deleted subgraphs have spectra bounded from below by −2

We consider the problem of reconstructing the characteristic polynomial of a graph from its polynomial deck, i.e. the collection of characteristic polynomials of its vertex-deleted subgraphs. Here we provide a positive answer to this problem for graphs as in the title, provided they are disconnected. Since the same problem for connected graph was already answered in positive, we have arrived at the positive answer for the entire collection of graphs under considerations.