Signless Laplacians and line graphs

D. Cvetković

The spectrum of a graph is the spectrum of its ađacency matrix. Cospectral graphs are graphs having the same spectrum. In this paper we study the phenomenon of cospectrality in graphs by comparing characterizing properties of spectra of graphs and spectra of their line graphs. We present some arguments showing that the latter perform better. In this comparison we use spectra of signless Laplacians of graphs.