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浙江大学学报(理学版)  2017, Vol. 44 Issue (3): 253-260,280    DOI: 10.3785/j.issn.1008-9497.2017.03.001
数学与计算机科学     
若干运算图的倍乘赋权Harary指标
温艳清1, 刘宝亮1, 安明强2
1. 山西大同大学 数学与计算机科学学院, 山西 大同 037009;
2. 天津科技大学 理学院, 天津 300457
Multiplicatively weighted Harary index of some graph operations
WEN Yanqing1, LIU Baoliang1, AN Mingqiang2
1. College of Mathematics and Computer Science, Shanxi Datong University, Datong 037009, Shanxi Province, China;
2. College of Science, Tianjin University of Science and Technology, Tianjin 300457, China
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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HMG)=ΣuvδGuδGv))(dGu,v)),其中,δGu)表示顶点u在图G中的度,dGu,v)表示2个顶点uv在图G中的距离.给出了张量积G×Kr,强积GKr,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.
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: HM(G)=Σuv(δG(u)δG(v))(dG(u,v)), where δG(u) denotes the degree of the vertex u in the graph G and dG(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×Kr, the strong product GKr 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 Kr 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 出版日期: 2017-03-01
CLC:  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.
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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.

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

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