The hyper-Zagreb index and some graph operations

Abstract

Let G be a simple connected graph. The Hyper-Zagreb index is defined as $$\textit{HM}(G)=\sum _{uv\in E_{G}}(d_{G}(u)+d_{G}(v))^2$$ . In this paper some exact expressions for the hyper-Zagreb index of graph operations containing cartesian product and join of n graphs, splice, link and chain of graphs will be presented. We also apply these results to some graphs to chemical and general interest, such as $$C_4$$ nanotube, rectangular grid, prism, complete n-partite graph.