Upper bounds on the Laplacian spread of graphs

Abstract

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.