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. L., New upper and lower bounds for the additive degree-Kirchhoff index, <<CROATICA CHEMICA ACTA>>, 2013; 86 (4): 363-370. [doi:10.5562/cca2282] [http://hdl.handle.net/10807/49836]
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
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