The Signless Laplacian Spectral Radii and Spread of Bicyclic Graphs

摘要

The signless Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the smallest eigenvalue of its signless Laplacian matrix. In this paper, we determine the first to 11th largest signless Laplacian spectral radii in the class of bicyclic graphs with n vertices. Moreover, the unique bicyclic graph with the largest or the second largest signless Laplacian spread among the class of connected bicyclic graphs of order n is determined, respectively.