The hyper-Zagreb index and some graph operations

被引：0
作者：
Wei Gao
Muhammad Kamran Jamil
Mohammad Reza Farahani
机构：
[1] Yunnan Normal University,School of Information Science and Technology
[2] Riphah International University,Department of Mathematics, Riphah Institute of Computing and Applied Sciences (RICAS)
[3] Department of Applied Mathematics of Iran University of Science and Technology (IUST),undefined
来源：
Journal of Applied Mathematics and Computing | 2017年 / 54卷
关键词：
The hyper-Zagreb index; Graph operations; nanotube; Rectangular grid; Primary: 05C76; Secondary: 05C90; 13;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let G be a simple connected graph. The Hyper-Zagreb index is defined as HM(G)=∑uv∈EG(dG(u)+dG(v))2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textit{HM}(G)=\sum _{uv\in E_{G}}(d_{G}(u)+d_{G}(v))^2$$\end{document}. 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 C4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_4$$\end{document} nanotube, rectangular grid, prism, complete n-partite graph.
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页码：263 / 275
页数：12
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