若干运算图的倍乘赋权Harary指标

doi:10.3785/j.issn.1008-9497.2017.03.001

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摘要 ALIZADEH等近期提出了一个修正的Harary指标，即顶点对的贡献被赋予其度的乘积.其指标被称为倍乘赋权Harary指标，定义为H_M（G）=Σ_u≠v（δ_G（u）δ_G（v））（d_G（u，v）），其中，δ_G（u）表示顶点u在图G中的度，d_G（u，v）表示2个顶点u和v在图G中的距离.给出了张量积G×K_r，强积G

K_r，圈积G₁oG₂的倍乘赋权Harary指标值的精确计算公式，这些公式与图的其他不变量（如倍加赋权Harary指标、Harary指标、第1类和第2类Zagreb指标、第1类和第2类反Zagreb指标）有关.此外，利用所得结果计算了开栅栏与闭栅栏的倍乘赋权Harary指标.

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	温艳清
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关键词 ：倍乘赋权Harary指标, Harary指标, 张量积, 强积, 圈积

Abstract：Recently, ALIZADEH et al proposed a modification of the Harary index in which the contributions of vertex pairs were weighted by the product of their degrees. It is named multiplicatively weighted Harary index and defined as: H_M(G)=Σ_u≠v(δ_G(u)δ_G(v))(d_G(u,v)), where δ_G(u) denotes the degree of the vertex u in the graph G and d_G(u,v) denotes the distance between two vertices u and v in the graph G. In this paper, the explicit formulae for the multiplicatively weighted Harary index of tensor product G×K_r, the strong product G

K_r and the wreath product G₁oG₂ in terms of other graph invariants including additively weighted Harary index, Harary index, the first and the second Zagreb indices and the first and the second Zagreb coindices, are obtained, where K_r is the complete graph. Additionally, we apply our results to compute the multiplicatively weighted Harary index of open fence and closed fence graphs.

Key words： multiplicatively weighted Harary index Harary index tensor product strong product wreath product

收稿日期: 2015-10-16

ZTFLH:

O157.5

基金资助:Supported by the Doctoral Scientific Research Foundation of Shanxi Datong University （2015-B-06）.

通讯作者: AN Mingqiang,ORCID:http://orcid.org/0000-0002-1105-750X,E-mail:anmq@tust.edu.cn. E-mail: anmq@tust.edu.cn

作者简介: WEN Yanqing(1980-),ORCID:http://orcid.org/0000-0002-9573-7245,female,doctoral student,lecture,the field of interest are reliability and graph theory,E-mail:oryqwen@163.com.

引用本文:

温艳清, 刘宝亮, 安明强. 若干运算图的倍乘赋权Harary指标[J]. 浙江大学学报（理学版）, 2017, 44(3): 253-260,280.
WEN Yanqing, LIU Baoliang, AN Mingqiang. Multiplicatively weighted Harary index of some graph operations. Journal of ZheJIang University(Science Edition), 2017, 44(3): 253-260,280.

链接本文:

http://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.03.001 或 http://www.zjujournals.com/sci/CN/Y2017/V44/I3/253

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