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Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs

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  • Wei Gao
  • Muhammad Kamran Jamil
  • Aisha Javed
  • Mohammad Reza Farahani
  • Shaohui Wang
  • Jia-Bao Liu

Abstract

The hyper-Zagreb index is an important branch in the Zagreb indices family, which is defined as , where is the degree of the vertex in a graph . In this paper, the monotonicity of the hyper-Zagreb index under some graph transformations was studied. Using these nice mathematical properties, the extremal graphs among -vertex trees (acyclic), unicyclic, and bicyclic graphs are determined for hyper-Zagreb index. Furthermore, the sharp upper and lower bounds on the hyper-Zagreb index of these graphs are provided.

Suggested Citation

  • Wei Gao & Muhammad Kamran Jamil & Aisha Javed & Mohammad Reza Farahani & Shaohui Wang & Jia-Bao Liu, 2017. "Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-5, February.
    • Handle: RePEc:hin:jnddns:6079450
    DOI: 10.1155/2017/6079450
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