Tian, Jing; Peng, Guiqin; Pei, Lidan; Pan, Xiangfeng On the multiplicatively weighted Harary index of composite graphs. (English) Zbl 1474.05096 J. Univ. Sci. Technol. China 50, No. 3, 261-270 (2020). Summary: Let \({H_M} (G)\) be the multiplicatively weighted Harary index of the molecular graph \(G\), which is defined as \({H_M} (G) = \sum\limits_{\{u,v\} \subseteq V (G)} \frac{{d_G} (u){d_G} (v)}{{d_G} (u,v)}\), where \({d_G} (u)\) is the degree of a vertex \(u \in V (G)\), 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 are determined for the multiplicatively weighted Harary index among graphs in each of the four classes of composite graphs. MSC: 05C09 Graphical indices (Wiener index, Zagreb index, Randić index, etc.) 05C07 Vertex degrees 05C76 Graph operations (line graphs, products, etc.) 05C92 Chemical graph theory 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.) Keywords:multiplicatively weighted Harary index; composite graph; graph operations; regular graph PDFBibTeX XMLCite \textit{J. Tian} et al., J. Univ. Sci. Technol. China 50, No. 3, 261--270 (2020; Zbl 1474.05096) Full Text: DOI