Aα-spectrum of duplicate and corona operations in graphs

Abstract

Let G be a graph of order n, A(G) its adjacency matrix and D(G) the diagonal matrix of degrees of G. In 2017, for every α in [0, 1], Nikiforov defined the matrix Aα(G) = αD(G) + (1 − α)A(G). In this paper, we investigate the Aα-spectrum of graphs obtained from the duplicate and corona operations. As an application of our results, we provide conditions for the construction of some pairs of non isomorphic Aα-cospectral graphs.