A Note on Reconstructing the Characteristic Polynomial of a Graph

Abstract

It is well known that the characteristic polynomial of any graph is determined up to an additive constant from its polynomial deck, i.e. the collection of the characteristic polynomials of the point deleted subgraphs. Here we prove that these constants are equal for any two connected graphs with the same polynomial decks, whenever the spectra of all subgraphs are bounded from below by -2.