On the multiplicatively weighted Harary index of composite graphs

doi:10.3969/j.issn.0253-2778.2020.03.002

Journal of University of Science and Technology of China ›› 2020, Vol. 50 ›› Issue (3): 261-270.DOI: 10.3969/j.issn.0253-2778.2020.03.002

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On the multiplicatively weighted Harary index of composite graphs

TIAN Jing， PENG Guiqin， PEI Lidan2, PAN Xiangfeng

Received:2018-10-12 Revised:2019-10-30 Accepted:2019-10-30 Online:2020-03-31 Published:2019-10-30
Contact: PAN Xiangfeng
About author:TIAN Jing, female, born in 1993, Master candidate. Research field: Graph theory and its applications. E-mail: JingTian526@126.com

Abstract

Abstract: Let HM(G) be the multiplicatively weighted Harary index of the molecular graph G, which is defined as HM(G)=∑{u,v}V(G)dG(u)dG(v)dG(u,v), where dG(u) is the degree of a vertex u∈V(G), and the dG(u,v) denotes the distance between u and v in G. We introduce four graph operations and obtain explicit formulas for the values of multiplicatively weighted Harary index of composite graphs generated by the four graph operations. Based on this, a lower and an upper bound is determined for the multiplicatively weighted Harary index among graphs in each of the four classes of composite graphs.

Key words: multiplicatively weighted Harary index, composite graph, Graph operations, Regular graph

CLC Number:

O157.4

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On the multiplicatively weighted Harary index of composite graphs

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