Resumen de Some results on spectral distances of graphs

Irena M. Jovanovic

• Spectral distances of graphs related to some graph operations and modifications are considered. We show that the spectral distance between two graphs does not depend on their common eigenvalues, up to multiplicities. The spectral distance between some graphs with few distinct eigenvalues is computed and due to the results obtained one of the previously posed conjectures related to the A-spectral distances of graphs has been disproved. In order to investigate the cospectrality for special classes of graphs, we computed spectral distances and distance related graph parameters on several specially constructed sets of graphs.