RT Journal Article
T1 Spectral properties of geometric-arithmetic index
A1 Rodríguez García, José Manuel
A1 Sigarreta Almira, José María
AB 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.
PB Elsevier
SN 0096-3003
YR 2016
FD 2016-03-20
LK https://hdl.handle.net/10016/32620
UL https://hdl.handle.net/10016/32620
LA eng
NO This research was supported in part by a Grant from Ministerio de Economía y Competitividad (MTM 2013-46374-P), Spain, and a Grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México.
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RD 27 jul. 2024