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

Let $G_1⊛G_2$,$G_1\text{sqcupdot}{G}_2$ and $G_1\text{sqcupplus}{G}_2$ 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 $G_1⊛G_2$,$G_1\text{sqcupdot}{G}_2$ and $G_1\text{sqcupplus}{G}_2$ for regular graphs $G_1$ and $G_2$. As an application, we construct infinitely many pairs of $A_{\alpha }$-cospectral graphs.