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The hyper-Zagreb index and some graph operations

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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.

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Authors and Affiliations

  1. School of Information Science and Technology, Yunnan Normal University, Kunming, 650500, China

    Wei Gao

  2. Department of Mathematics, Riphah Institute of Computing and Applied Sciences (RICAS), Riphah International University, 14 Ali Road, Lahore, Pakistan

    Muhammad Kamran Jamil

  3. Department of Applied Mathematics of Iran University of Science and Technology (IUST), Narmak, Tehran, 16844, Iran

    Mohammad Reza Farahani

Authors
  1. Wei Gao
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  2. Muhammad Kamran Jamil
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  3. Mohammad Reza Farahani
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Correspondence to Mohammad Reza Farahani.

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Gao, W., Jamil, M.K. & Farahani, M.R. The hyper-Zagreb index and some graph operations. J. Appl. Math. Comput. 54, 263–275 (2017). https://doi.org/10.1007/s12190-016-1008-9

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  • DOI: https://doi.org/10.1007/s12190-016-1008-9

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