$A_\alpha$-SPECTRA OF DUPLICATION CORONAS

The convex combination of diagonal matrix $D(G)$ and adjacency matrix $A(G)$ defined as $A_\alpha(G)=\alpha D(G)+(1-\alpha)A(G) \textrm{for} \alpha \in [0,1] $ is indeed a good choice to merge $A$-spectra and $Q$-spectra theories of graphs. In this work, we discuss $A_\alpha$-eigenvalues of duplication corona, duplication edge corona, duplication neighbourhood corona and vertex complemented corona. Motivated by these operations, we have defined duplication vertex complemented corona operation and obtained corresponding $A_\alpha$-eigenvalues. We have also suggested some infinite family of graphs based on these findings.