Extremal properties of graphs and eigencentrality in trees with a given degree sequence

Anna Torriero, Silvana Stefani, Rosanna Grassi

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13 Citazioni (Scopus)

Abstract

In this article, we investigate several issues related to the use of the index S(G), known as the Zagreb index (see Gutman and Das, 2004) or “S-metric” (Alderson and Li, 2007). We present some new upper and lower bounds for S(G), in terms of the degree sequence of G. Then, we concentrate on trees and prove that in trees with maximum S(G) the eigenvector ordering is coherent with the degree ordering; that is, degree central vertices are also eigenvector central. This confirms results given in Bonacich (2007). Further, we show that these trees have minimum diameter and maximum spectral radius in the set of trees with a given degree sequence. A simple application to a company organizational network is provided.
Lingua originaleEnglish
pagine (da-a)115-135
Numero di pagine21
RivistaTHE JOURNAL OF MATHEMATICAL SOCIOLOGY
Volume34
DOI
Stato di pubblicazionePubblicato - 2010

Keywords

  • bounds
  • degree sequence
  • diameter
  • eigenvector centrality
  • graphs

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