×

On the multiplicatively weighted Harary index of composite graphs. (English) Zbl 1474.05096

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.)
PDFBibTeX XMLCite
Full Text: DOI