The Augmented Zagreb Indices of Fluoranthene-Type Benzenoid Systems

Abstract

The augmented Zagreb index (AZI index) of a graph $$G=(V,E)$$ , which is a valuable predictive index in the study of the heat of formation in octanes and heptanes, is defined as $$\begin{aligned} \hbox {AZI}(G)=\sum _{uv\in E(G)}\left( \frac{d_{u}d_{v}}{d_{u}+d_{v}-2}\right) ^{3}{,} \end{aligned}$$ where $$d_{u}$$ and $$d_{v}$$ are the degrees of the terminal vertices u and v of edge uv, respectively. In this paper, we give the expressions for computing the augmented Zagreb indices of fluoranthene-type benzenoid systems, and we determine the extremal values of augmented Zagreb index in f-benzenoid systems with h hexagons. Especially, we give the extremal values of augmented Zagreb index in cata-catacondensed fluoranthene-type benzenoid systems with h hexagons.