The minimum signless Laplacian spread ofunicyclic graphs

By using the interlacing theorem of the signless Laplacian eigenvalues, the relationship on the signless Laplacian spread of a graph and an pendent vertex-deleted subgraph is established. Combined the graph operation of gradually deleting pendent vertices of uncyclic graph, and calculated the signless Laplacian spread of some special unicyclic graphs, the graph with minimum signless Laplacian spread is determined among the class of unicyclic graphs with n vertices.