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arXiv · 1311.3113

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

Monica Bianchi·Alessandra Cornaro·José Luis Palacios·Anna Torriero
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Abstract

Given a simple connected graph on $N$ vertices with size $|E|$ and degree sequence $d_{1}\leq d_{2}\leq ...\leq d_{N}$, 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.

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Monica Bianchi, Alessandra Cornaro, José Luis Palacios, Anna Torriero. 2013-11-13. New upper and lower bounds for the additive degree-Kirchhoff index. https://doi.org/10.5562/cca2282

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