Graph Cospectrality using Neighborhood Matrices

A Bessa, I Rocha-Neto, S Pinho, R Andrade, T Lobao
In this note we address the problem of graph isomorphism by means of eigen-value spectra of different matrix representations: the neighborhood matrixˆMmatrixˆ matrixˆM , its corresponding signless Laplacian Q ˆ M , and the set of higher order adjacency matrices M s. We find that, in relation to graphs with at most 10 vertices, Q ˆ M leads to better results than the signless Laplacian Q; besides, when combined withˆMwithˆ withˆM , it even surpasses the Godsil and McKay switching method.