Sharp Bounds on the Augmented Zagreb Index of Graph Operations

N. Dehgardi, H. Aram

Let $G$ be a finite and simple graph with edge set $E(G)$. The { augmented Zagreb index} of $G$ is $$AZI(G)=um_{uvı E(G)}eft(\frac{d_{G}(u)d_{G}(v)}{d_{G}(u)+d_{G}(v)-2}\right)^3,$$ where $d_{G}(u)$ denotes the degree of a vertex $u$ in $G$. In this paper, we give some bounds of this index for join, corona, cartesian and composition product of graphs by general sum-connectivity index and general Randić index and compute the sharp amount of that for the regular graphs.