Bounding the Sum of Powers of Normalized Laplacian Eigenvalues of Graphs through Majorization Methods

Monica Bianchi, Anna Torriero, Alessandra Cornaro, José Luis Palacios

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)707-716
Number of pages10
JournalMatch
Volume70
Publication statusPublished - 2013

Keywords

  • Schur-convex functions
  • expected hitting times
  • majorization

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