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

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

Discrete Dynamics in Nature and Society, 2017, vol. 2017, 1-5

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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:6079450

DOI: 10.1155/2017/6079450

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