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

Abstract

Given a simple connected graph on $N$ vertices with size $|E|$ and degree sequence $d_1\le d_2\le ...\le d_N$, 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 $d_i$) 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.

Cited by in corpus (1)

• New bounds of degree-based topological indices for some classes of $c$-cyclic graphs