Complementary Signless Laplacian Equienergetic Graphs

Graph energy is a classical spectral invariant, and the study of Laplacian-type energies extends thisidea from adjacency spectra to degree-sensitive matrix spectra. In particular, the signless Laplacianmatrix Q(G) = D(G)+A(G) is useful for studying structural properties that are not captured bythe adjacency spectrum alone. The signless Laplacian energy is defined by the deviations ofthe Q-eigenvalues from the average degree, and has been investigated through bounds, extremalproblems, and relations with other graph energies.