On Eigenvalues and Energy of Geometric–Arithmetic Matrix of Graphs

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

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

Let G be a graph with vertex set { v1, v2, … , vn} and let di denote the degree of vertex vi. The geometric–arithmetic matrix GA(G) of G is indexed by the vertices of G, whose (i, j) -th entry is 2didjdi+dj if the vertices i and j are adjacent and 0 otherwise. The multi-set of eigenvalues of GA(G) is known as the geometric–arithmetic spectrum of G. In this article, we obtain geometric–arithmetic spectra of various families of graphs and characterize the connected graphs with two and three distinct GA eigenvalues. We obtain several upper and lower bounds for the geometric arithmetic energy and characterize the graphs attaining such bounds.

Original languageEnglish
Article number115
JournalMediterranean Journal of Mathematics
Volume19
Issue number3
DOIs
Publication statusPublished - Jun 2022

Keywords

  • Adjacency matrix
  • energy
  • geometric–arithmetic eigenvalues
  • geometric–arithmetic index

ASJC Scopus subject areas

  • Mathematics(all)

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