Let G be a graph of order $n$ with adjacency matrix $A(G)$ and diagonal matrix of degree $D(G)$. For every $α\in [0,1]$, Nikiforov \cite{VN17} defined the matrix $A_α(G) = αD(G) + (1-α)A(G)$. In this paper we present the $A_α(G)$-characteristic polynomial when $G$ is obtained by coalescing two graphs, and if $G$ is a semi-regular bipartite graph we obtain the $A_α$-characteristic polynomial of the line graph associated to $G$. Moreover, if $G$ is a regular graph we exhibit the $A_α$-characteristic polynomial for the graphs obtained from some operations.