In this paper we present a theoretical analysis in order to establish maximal and minimal vectors with respect to the majorization order of particular subsets of Ân. Afterwards we apply these issues to the calculation of bounds for a topological descriptor of a graph known as the second Zagreb index. Finally, we show how our bounds may improve the results obtained in the literature, providing some theoretical and numerical examples.
Bianchi, M., Cornaro, A., Torriero, A. (2013). Majorization under constraints and bounds on the second Zagreb index. MATHEMATICAL INEQUALITIES & APPLICATIONS, 16(2), 329-347 [10.7153/mia-16-25].
Majorization under constraints and bounds on the second Zagreb index
Bianchi, Monica;Cornaro, Alessandra;Torriero, Anna
2013
Abstract
In this paper we present a theoretical analysis in order to establish maximal and minimal vectors with respect to the majorization order of particular subsets of Ân. Afterwards we apply these issues to the calculation of bounds for a topological descriptor of a graph known as the second Zagreb index. Finally, we show how our bounds may improve the results obtained in the literature, providing some theoretical and numerical examples.
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