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
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)=Σu≠v(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.
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.
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