New upper and lower bounds for the additive degree-Kirchhoff index

Given a simple connected graph on N vertices with size |E|\r\n and degree sequence d₁≤d₂≤...≤dn, the aim of this paper is\r\n to exhibit new upper and lower bounds for the additive degree-\r\nKirchhoff index in closed forms, not containing effective resistances \r\nbut a few invariants (N,|E| and the degrees di) and applicable in\r\n general contexts. In our arguments we follow a dual approach: \r\nalong with a traditional toolbox of inequalities we also use a relatively \r\nnewer method in Mathematical Chemistry, based on the majorization\r\n and Schur-convex functions. Some theoretical and numerical \r\nexamples are provided, comparing the bounds obtained here and\r\nthose previously known in the literature