On spectra of variants of the corona of two graphs and some new equienergetic graphs

Aα-spectrum of duplicate and corona operations in graphs

“…The extremal problems for the largest and the second largest α-eigenvalues were studied in [8,17,23,24,28,29]. Many graph operations such as disjoint union, corona, edge corona, neighborhood corona, common neighborhood graphs, have been introduced and their spectral properties have been studied, see [1,3,5,9,10,12,14,15,16,18,19,26]. Several variants of corona product and duplicate of two graphs have been introduced and their spectra are computed.…”

“…Several variants of corona product and duplicate of two graphs have been introduced and their spectra are computed. In 2018, Adiga et al [2] introduced duplication corona, duplication neighborhood corona and duplication edge corona of two graphs and studied their adjacency spectrum, Laplacian spectrum and signless Laplacian spectrum. In this paper, we investigate the A α -spectrum of these operations on graphs, and as an application of our results, we provide conditions for the construction of some pairs of non isomorphic A α -cospectral graphs.…”

On A-energy and S-energy of certain class of graphs

“…Ramane et al [21] obtained non-cospectral A-equienergetic iterated line graphs from regular graphs. For other results on A-equienergetic and Sequienergetic graphs one can see [1,4,7,11,12,13,14,15,18,22,24]. For other notation, terminology and results related to the spectra of graphs we follow [6].…”