Upper bounds on the Laplacian spread of graphs

The Laplacian spread of a graph G is defined as the difference between the largest and the second smallest eigenvalue of the Laplacian matrix of G. In this work, an upper bound for this graph invariant, that depends on first Zagreb index, is given. Moreover, another upper bound is obtained and expressed as a function of the nonzero coefficients of the Laplacian characteristic polynomial of a graph.