More Inequalities for Laplacian Indices by Way of Majorization

The n-tuple of Laplacian characteristic values of a graph is majorized by the conjugate sequence of its degrees . Using that result we find a collection of general inequalities for a number of Laplacian indices expressed in terms of the conjugate degrees , and then with a maximality argument , we find tight general bounds expressed in terms of the size of the vertex set n and the average degree dg = 2/E|/n . We also find some particular tight bounds for some classes of graphs in terms of customary graph parameters .