Spectral determination of graphs whose components are paths and cycles

Abstract

We consider the class of graphs each of whose components is either a path or a cycle. We classify the graphs from the class considered into those which are determined and those which are not determined by the adjacency spectrum. In addition, we compare the result with the corresponding results for the Laplacian and the signless Laplacian spectra. It turns out that the signless Laplacian spectrum performs the best, confirming some expectations from the literature.