New bounds for the sum of powers of normalized Laplacian eigenvalues of graphs

Gian Paolo Clemente, Alessandra Cornaro

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

For a simple and connected graph, a new graph invariant s(G), defined as the sum of alpha-powers of the eigenvalues of the normalized Laplacian matrix, has been introduced by Bozkurt and Bozkurt (2012). Lower and upper bounds for this index have been proposed by the authors. In this paper, we localize the eigenvalues of the normalized Laplacian matrix by adapting a theoretical method, proposed in Bianchi and Torriero (2000), based on majorization techniques. Through this approach we derive upper and lower bounds of s(G). Some numerical examples show how sharper results can be obtained with respect to those existing in literature.
Original languageEnglish
Pages (from-to)403-413
Number of pages11
JournalArs Mathematica Contemporanea
Volume11
Publication statusPublished - 2016

Keywords

  • Bounds
  • Graphs
  • Majorization
  • Topological Indices

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