In this note, we use a procedure, proposed in [Bianchi, M., and A. Torriero, Some localization theorems using a majorization technique, Journal of Inequalities and Applications 5 (2000), 433-446], based on a majorization technique, which localizes real eigenvalues of a matrix of order n. Through this information, we compute a lower bound for the Kirchhoff index (see [Bianchi M., A. Cornaro, J.L. Palacios and A. Torriero, Bounds for the Kirkhhoff index via majorization techniques, Journal of Mathematical Chemistry, (2012) online first]) that takes advantage of additional eigenvalues bounds. An algorithm has been developed with MATLAB software to evaluate the above mentioned bound. Finally, numerical examples are provided showing how tighter results can be obtained.

Cornaro, A., Clemente, G. (2013). A New Lower Bound for the Kirchhoff Index using a numerical procedure based on Majorization Techniques. ELECTRONIC NOTES IN DISCRETE MATHEMATICS, 41, 383-390 [10.1016/j.endm.2013.05.116].

A New Lower Bound for the Kirchhoff Index using a numerical procedure based on Majorization Techniques

Cornaro, Alessandra
;
2013

Abstract

In this note, we use a procedure, proposed in [Bianchi, M., and A. Torriero, Some localization theorems using a majorization technique, Journal of Inequalities and Applications 5 (2000), 433-446], based on a majorization technique, which localizes real eigenvalues of a matrix of order n. Through this information, we compute a lower bound for the Kirchhoff index (see [Bianchi M., A. Cornaro, J.L. Palacios and A. Torriero, Bounds for the Kirkhhoff index via majorization techniques, Journal of Mathematical Chemistry, (2012) online first]) that takes advantage of additional eigenvalues bounds. An algorithm has been developed with MATLAB software to evaluate the above mentioned bound. Finally, numerical examples are provided showing how tighter results can be obtained.
Articolo in rivista - Articolo scientifico
Graphs; Kirchhoff index; Majorization order
English
383
390
8
Cornaro, A., Clemente, G. (2013). A New Lower Bound for the Kirchhoff Index using a numerical procedure based on Majorization Techniques. ELECTRONIC NOTES IN DISCRETE MATHEMATICS, 41, 383-390 [10.1016/j.endm.2013.05.116].
Cornaro, A; Clemente, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/334322
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