Spectral study of the Geometric-Arithmetic Index

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. Supported in part by a grant from Ministerio de Economía y Competititvidad (MTM 2013-46374-P), Spain, and by a grant from CONACYT (CONACYT-UAG I0110/62/10), México. Publicado