Aα spectra of graphs obtained by two corona operations and Aα cospectral graphs.

Let G be a graph of which A be the adjacency matrix and D be a diagonal matrix whose diagonal entries are the degrees of vertices of G. Q = A + D is known as the signless Laplacian matrix of the graph G. For any real α ∈ [ 0 , 1 ] , A α matrix is defined by the convex combination α D + (1 − α) A of D and A. Clearly, A α coincides with A for α = 0 and coincides with Q / 2 for α = 1 / 2. Thus, the A α eigenvalues are generalizations of adjacency eigenvalues and signless Laplacian eigenvalues. In this paper, we have obtained the A α spectra of corona and edge corona of two graphs. We have also shown that A α cospectral graphs and α equienergetic graphs can be obtained from there. [ABSTRACT FROM AUTHOR]