On the Distance Spectral Radius of Trees with Given Degree Sequence

Kenneth Dadedzi, Valisoa Razanajatovo Misanantenaina, Stephan Wagner

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We consider the problem of maximizing the distance spectral radius and a slight generalization thereof among all trees with some prescribed degree sequence. We prove in particular that the maximum of the distance spectral radius has to be attained by a caterpillar for any given degree sequence. The same holds true for the terminal distance matrix. Moreover, we consider a generalized version of the reverse distance matrix and also study its spectral radius for trees with given degree sequence. We prove that the spectral radius is always maximized by a greedy tree. This implies several corollaries, among them a "reversed" version of a conjecture of Stevanović and Ilić. Our results parallel similar theorems for the Wiener index and other invariants.

Original languageEnglish
Pages (from-to)495-524
Number of pages30
JournalDiscussiones Mathematicae - Graph Theory
Volume40
Issue number2
DOIs
Publication statusPublished - 1 May 2020
Externally publishedYes

Keywords

  • degree sequence
  • distance matrix
  • spectral radius
  • tree

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