On the Aα-characteristic polynomial of a graph

In this paper, we first formulate the first four coefficients cα0(G), cα1(G), cα2(G) and cα3(G) of the Aα-characteristic polynomial of G. And then, we observe that Aα-spectra are much efficient for us to distinguish graphs, by enumerating the Aα-characteristic polynomials for all graphs on at most 10 vertices. To verify this observation, we characterize some graphs determined by their Aα-spectra.