Majorization bounds for signless Laplacian eigenvalues

Abstract

It is known that, for a simple graph G and a real number a, the quantity s'α (G) is defined as the sum of the α-th power of non-zero singless Laplacian eigenvalues of G. In this paper, first some majorization bounds over s'α(G) are presented in terms of the degree sequences, and number of vertices and edges of G. Additionally, a connection between s'α(G) and the first Zagreb index, in which the Holder's inequality plays a key role, is established. In the last part of the paper, some bounds (included Nordhauss-Gaddum type) for signless Laplacian Estrada index are presented.