Constructions of $A_\alpha$-cospectral graphs using some corona operations

Let $G_1 \circledast G_2$,$G_1 \sqcupdot G_2$ and $G_1 \sqcupplus G_2$ denote the total corona, $Q$-vertex corona and $Q$-edge corona of two graphs $G_1$ and $G_2$, respectively. In this paper, we compute the $A_\alpha$-spectrum of $G_1 \circledast G_2$,$G_1 \sqcupdot G_2$ and $G_1 \sqcupplus G_2$ for regular graphs $G_1$ and $G_2$. As an application, we construct infinitely many pairs of $A_\alpha$-cospectral graphs.