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Let G be a simple connected graph. The Hyper-Zagreb index is defined as $$\textit{HM}(G)=\sum _{uv\in E_{G}}(d_{G}(u)+d_{G}(v))^2$$HM(G)=∑uv∈EG(dG(u)+dG(v))2. In this paper some exact expressions for the hyper-Zagreb index of graph operations containing… Click to show full abstract
Let G be a simple connected graph. The Hyper-Zagreb index is defined as $$\textit{HM}(G)=\sum _{uv\in E_{G}}(d_{G}(u)+d_{G}(v))^2$$HM(G)=∑uv∈EG(dG(u)+dG(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 $$C_4$$C4 nanotube, rectangular grid, prism, complete n-partite graph.
Journal Title: Journal of Applied Mathematics and Computing
Year Published: 2017
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