Majorization under constraints and bounds of the second Zagreb index
  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 \Re ^n: Afterwards we apply these issues to the calcula- tion of bounds for a topological descriptor of a graph known as the second Zagreb index. Finally, we show how our bounds may improve the re- sults obtained in the literature, providing some theoretical and numerical examples. 
Monica Bianchi, Alessandra Cornaro and Anna Torriero
math.CO math.OC