Graph cospectrality using neighborhood matrices

Abstract

In this note we address the problem of graph isomorphism by means of eigenvalue spectra of different matrix representations: the neighborhood matrix M̂, its corresponding signless Laplacian QM̂, and the set of higher order adjacency matrices Mℓs. We find that, in relation to graphs with at most 10 vertices, QM̂ leads to better results than the signless Laplacian Q; besides, when combined with M̂, it even surpasses the Godsil and McKay switching method.