New bounds for the spread of the signless Laplacian spectrum

Eigenvalue Bounds for the Signless Laplacian

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.

Majorization bounds for signless Laplacian eigenvalues

Sharp bounds for the signless Laplacian spectral radius of digraphs

New Theorems for Signless Laplacian Eigenvalues

AMS Mathematics Subject Classification (2000): 05C50

The Signless Laplacian Estrada Index of Unicyclic Graphs

‎For a simple graph $G$‎, ‎the signless Laplacian Estrada index is defined as $SLEE(G)=sum^{n}_{i=1}e^{q^{}_i}$‎, ‎where $q^{}_1‎, ‎q^{}_2‎, ‎dots‎, ‎q^{}_n$ are the eigenvalues of the signless Laplacian matrix of $G$‎. ‎In this paper‎, ‎we first characterize the unicyclic graphs with the first two largest and smallest $SLEE$'s and then determine the unique unicyclic graph with maximum $SLEE$ a...