Spectral properties of geometric-arithmetic index Articles uri icon

publication date

  • March 2016

start page

  • 142

end page

  • 153

volume

  • 277

international standard serial number (ISSN)

  • 0096-3003

electronic international standard serial number (EISSN)

  • 1873-5649

abstract

  • 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 reflected in the algebraic properties of some matrices. The aim of this paper is to study the geometric-arithmetic index GA(1) 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. Moreover, using this matrix, we define a GA Laplacian matrix which determines the geometric-arithmetic index of a graph and satisfies properties similar to the ones of the classical Laplacian matrix. (C) 2015 Elsevier Inc. All rights reserved.

keywords

  • geometric arithmetic index; spectral properties; laplacian matrix; laplacian eigenvalues; topological index; graph invariant; pi-electron energy; zagreb indexes; laplacian energy; randic index; tricyclic graphs; maximal energy; bounds