Nordhaus–Gaddum and other bounds for the sum of squares of the positive eigenvalues of a graph

Clive Elphick, Mustapha Aouchiche

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Terpai [21] proved the Nordhaus–Gaddum bound that μ(G)+μ(G‾)≤4n/3−1, where μ(G) is the spectral radius of a graph G with n vertices. Let s+ denote the sum of the squares of the positive eigenvalues of G. We prove that s+(G)+s+(G‾)2n and conjecture that s+(G)+s+(G‾)≤4n/3−1. We have used AutoGraphiX and Wolfram Mathematica to search for a counter-example. We also consider Nordhaus–Gaddum bounds for s+ and bounds for the Randić index.

Original languageEnglish
Pages (from-to)150-159
Number of pages10
JournalLinear Algebra and Its Applications
Volume530
DOIs
Publication statusPublished - Oct 1 2017
Externally publishedYes

Keywords

  • Eigenvalues
  • Graph
  • Nordhaus–Gaddum relations
  • Randic index

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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