Spectral Generalizations of Line Graphs: On Graphs with Least Eigenvalue -2

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Towards a spectral theory of graphs based on the signless Laplacian, I (2009, methodology): “Moreover, connection with spectra of line graphs and the existence of a well developed theory of graphs with least eigenvalue −2 [8] were used as additional arguments for studying eigenvalues of the signless Laplacian.”
Signless Laplacians of finite graphs (2007, background): “The well developed theory of graphs with least eigenvalue −2 (see [2]) supports the idea that, among matrices associated with a graph (generalized adjacency matrices), the signless Laplacian seems to be the most convenient for use in studying graph properties.”
Graphs for which the least eigenvalue is minimal, II (2008, background): “Graphs with least eigenvalue not less than −2 are studied extensively in the literature (see [8] for details).”
Old and new results on algebraic connectivity of graphs (2007, background): “The adjacency matrix and its eigenvalues have been investigated more than the Laplacian matrix, see [6,14,17,18], and according to Mohar [64] the Laplacian eigenvalues are more intuitive and much more important than the spectrum of the adjacency matrix.”