The augmented Zagreb index of the catacondensed hexagonal systems

Abstract

The augmented Zagreb index (AZI) of a graph G=(V, E) was recently introduced by FURTULA et al, which is defined as \begin{document}${\rm{AZI}}(G)=\sum\limits_{uv \in E (G)} {{{\left ({\frac{{{d_u}{d_v}}}{{{d_u} + {d_v} -2}}} \right)}^3}} $\end{document} , where du denotes the degree of a vertex u in 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.