On the spread of the geometric-arithmetic matrix of graphs

Bilal A. Rather, M. Aouchiche, S. Pirzada

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In a graph G, if di is the degree of a vertex vi, the geometric-arithmetic matrix GA(G) is a square matrix whose (Formula presented.) -th entry is (Formula presented.) whenever vertices i and j are adjacent and 0 otherwise. The set of all eigenvalues of GA(G) including multiplicities is known as the geometric-arithmetic spectrum of G. The difference between the largest and the smallest geometric-arithmetic eigenvalue is called the geometric-arithmetic spread (Formula presented.) of G. In this article, we investigate some properties of (Formula presented.) We obtain lower and upper bounds of (Formula presented.) and show the existence of graphs for which equality holds. Further, (Formula presented.) is computed for various graph operations.

Original languageEnglish
Pages (from-to)146-153
Number of pages8
JournalAKCE International Journal of Graphs and Combinatorics
Volume19
Issue number2
DOIs
Publication statusPublished - 2022

Keywords

  • 05C12
  • 05C50
  • 15A18
  • Adjacency matrix
  • geometric-arithmetic index
  • geometric-arithmetic spectrum
  • spectral radius
  • spread

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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