Abstract
Let [Formula: see text] be a simple, connected graph. The matrix [Formula: see text] is defined as [Formula: see text], [Formula: see text], where [Formula: see text] is the adjacency matrix and [Formula: see text] is the degree matrix of [Formula: see text]. Let [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] denote the neighborhood corona, subdivision vertex corona, subdivision edge corona, central vertex corona and central edge corona of two graphs [Formula: see text] and [Formula: see text], respectively. In this paper, we determine the [Formula: see text]-characteristic polynomial and [Formula: see text]-spectra of non-regular graphs obtained from the above operations. As an application, we construct infinitely many pairs of non-regular [Formula: see text]-cospectral graphs. Also, we estimate the [Formula: see text]-energy of the graphs obtained by operating a regular graph [Formula: see text] and a non-regular graph, [Formula: see text].
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