Comparing the geometric–arithmetic index and the spectral radius of graphs

Mustapha Aouchiche, Pierre Hansen

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

The geometric-arithmetic index GA of a graph G is the sum of ratios, over all edges of G, of the geometric mean to the arithmetic mean of the end vertices degrees of an edge. The spectral radius λ1 of G is the largest eigenvalue of its adjacency matrix. These two parameters are known to be used as molecular descriptors in chemical graph theory. In the present paper, we compare GA and λ1 of a connected graph with given order. We prove, among other results, upper and lower bounds on the ratio GA/λ1 as well as a lower bound on the ratio GA/λ21. In addition, we characterize all extremal graphs corresponding to each of these bounds.

Original languageEnglish
Pages (from-to)473-482
Number of pages10
JournalMatch
Volume84
Issue number2
Publication statusPublished - 2020

ASJC Scopus subject areas

  • Chemistry(all)
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

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