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

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