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.

Torriero, A., Bianchi, M., Cornaro, A., & Palacios, J. (2013). New upper and lower bounds for the additive degree-Kirchhoff index. CROATICA CHEMICA ACTA, 86(4), 363-370 [10.5562/cca2282].

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

Torriero, Anna;Bianchi, Monica;Cornaro, Alessandra;
2013

Abstract

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.
Articolo in rivista - Articolo scientifico
Expected hitting times; Majorization; Schur-convex functions
English
363
370
8
Gold Open Access• Green Open Access
Torriero, A., Bianchi, M., Cornaro, A., & Palacios, J. (2013). New upper and lower bounds for the additive degree-Kirchhoff index. CROATICA CHEMICA ACTA, 86(4), 363-370 [10.5562/cca2282].
Torriero, A; Bianchi, M; Cornaro, A; Palacios, J
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/334320
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