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

被引：24

作者：

Gao, Wei ^{[1
]}

Jamil, Muhammad Kamran ^{[2
]}

Javed, Aisha ^{[3
]}

Farahani, Mohammad Reza ^{[4
]}

Wang, Shaohui ^{[5
]}

Liu, Jia-Bao ^{[6
]}

机构：

[1] Yunnan Normal Univ, Sch Informat Sci & Technol, Kunming 650500, Peoples R China

[2] Riphah Int Univ, RICAS, Lahore, Pakistan

[3] Govt Coll Univ, Abdus Salam Sch Math Sci, Lahore, Pakistan

[4] Iran Univ Sci & Technol, Dept Appl Math, Tehran, Iran

[5] Adelphi Univ, Dept Math & Comp Sci, Garden City, NY 11530 USA

[6] Anhui Jianzhu Univ, Sch Math & Phys, Hefei 230601, Peoples R China

来源：

DISCRETE DYNAMICS IN NATURE AND SOCIETY | 2017年 / 2017卷

关键词：

ENERGY;

D O I：

10.1155/2017/6079450

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The hyper-Zagreb index is an important branch in the Zagreb indices family, which is defined as Sigma(uv epsilon E(G)) (d(u) + (d(v))(2), where d(v) is the degree of the vertex V in a graph G = (V(G), E(G)). 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 n-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.

引用

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