Three distance characteristic polynomials of some graphs

摘要

We give complete information about the distance, distance Laplacian and distance signless Laplacian characteristic polynomials of graphs obtained by a generalized join graph operation on families of graphs. As an application of these results, we construct many pairs of nonisomorphic distance, distance Laplacian and distance signless Laplacian cospectral graphs, and then give a negative answer to the question "Can every connected graph be determined by its distance Laplacian spectrum and/or distance signless Laplacian spectrum?" proposed in Aouchiche and Hansen (2013) [2].