中文摘要：

FURTULA等提出了一个关于图G=（V,E）的增强型萨格勒布指数（AZI）,定义为AZI（G）=∑uv∈E（G）（d_ud_v/d_u＋d_v-2）~3,其中d_u表示图G的顶点u的度数.AZI已被证实在辛烷和正庚烷的生成热研究中是一个有价值的预测指数.对树状六角系统的AZI指数进行了讨论,给出了其AZI指数可达的上、下界.

英文摘要：

The augmented Zagreb index（AZI）of a graph G=（V,E）was recently introduced by FURTULA et al,which is defined as AZI（G）=∑uv∈E（G）（d_ud_v/d_u＋d_v-2）3,where du denotes the degree of a vertex uin G.The augmented Zagreb index has been proven to be a valuable predictive index in the study of the formation heat of octanes and heptanes.In this paper,the tight upper and lower bounds for AZI of the catacondensed hexagonal systems are obtained.