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
2013
86
4
363
370
none
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].
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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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