Spectral study of the Geometric-Arithmetic Index Articles uri icon

publication date

  • July 2015

start page

  • 121

end page

  • 135


  • 1


  • 74

International Standard Serial Number (ISSN)

  • 0340-6253


  • The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. One of the main aims of algebraic graph theory is to determine how, or whether, properties of graphs are reected in the algebraic properties of some matrices. The aim of this paper is to study the geometric-arithmetic index GA1 from an algebraic viewpoint. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix that is a modification of the classical adjacency matrix involving the degrees of the vertices.


  • geometric–arithmetic index; spectral properties; laplacian matrix; laplacian eigenvalues; topological index; graph invariant