Constructions of $A_{\hat{I}}\pm$-cospectral graphs using some corona operations

Abstract

Let $G_1⊛G_2$,$ 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 $A_{\hat{I}}\pm$-spectrum of $G_1⊛G_2$,$ 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 $A_{\hat{I}}\pm$-cospectral graphs.