Eigenvalue Bounds for the Signless Laplacian

Dragoš Cvetković, Peter Rowlinson, Slobodan Simić

We extend our previous survey of properties of spectra of signless Laplacians of graphs. Some new bounds for eigenvalues are given, and the main result concerns the graphs whose largest eigenvalue is maximal among the graphs with fixed numbers of vertices and edges. The results are presented in the context of a number of computer-generated conjectures.