Spectra and energies of iterated line graphs of regular graphs

The energy of integral circulant graphs with prime power order

“…Maximal energies to be found in special graph classes were studied by Balakrishnan [4] and Li et al [20] for kregular graphs, and by Shparlinksi [27] for circulant graphs. Let us note in passing that a surprising fact about line graph energies is that k-th iterated line graphs (k ≥ 2) of any two r-regular graphs (r ≥ 3) with the same number of vertices actually have the same energies, as shown by Ramane et al [24]. A graph G on n vertices is called hyperenergetic if its energy is greater than the energy of the complete graph on the same number of vertices, i.e.…”

Graphs with least eigenvalue −2: Ten years on

“…This fact can perhaps be explained by the high multiplicity of −2, which is in accordance with the main conclusion of [32] that maximal energy graphs should have a small number of distinct eigenvalues. The energy and some other spectral invariants of certain L-graphs are discussed in [56,65,72,75,84,85,86,132] in the context of Chemistry. In particular, the paper [132] deals with the eigenvalues of the distance matrix D of a graph and with the corresponding energy.…”

Energy of generalized line graphs

“…Line graph plays an important role in the study of graph theory. The energy, Laplacian energy, and signless Laplacian energy of line graphs were studied in [13,1,14,20]. Gutman et al established relations between energy of the line graph of a graph G and energies associated with the Laplacian and signless Laplacian matrices of G in [13].…”