Asymptotic normality for the coefficients of some graph polynomials

Let P(G, x) be a graph polynomial whose roots are all real and nonnegative, and let {Gh}h⩾1 be a sequence of simple graphs. We establish new algebraic and geometric conditions ensuring the asymptotic normality of the coe cient arrays associated with P(Gh, x). We then specialise our criteria to the Laplacian matching polynomial and to the characteristic polynomials of prominent positive semide nite matrices, including the signless Laplacian matrix, the normalized Laplacian matrix and its signless analogue, aswell as Nikiforov's Aα-matrix for 1/2 ⩽ α ⩽ 1. We further extend the frameworks to signed graphs and complex gain graphs.