University of IsfahanTransactions on Combinatorics2251-86572420131201Reciprocal degree distance of some graph operations1324350610.22108/toc.2013.3506ENKannanPattabiramanAnnamalai UniversityM.VijayaragavanThiruvalluvar College of Engineering and TechnologyJournal Article20130820The reciprocal degree distance (RDD), defined for a connected graph $G$ as vertex-degree-weighted sum of the reciprocal distances, that is, $RDD(G) =\sum\limits_{u,v\in V(G)}\frac{d_G(u) + d_G(v)}{d_G(u,v)}.$ The reciprocal degree distance is a weight version of the Harary index, just as the degree distance is a weight version of the Wiener index. In this paper, we present exact formulae for the reciprocal degree distance of join, tensor product, strong product and wreath product of graphs in terms of other graph invariants including the degree distance, Harary index, the first Zagreb index and first Zagreb coindex. Finally, we apply some of our results to compute the reciprocal degree distance of fan graph, wheel graph, open fence and closed fence graphs.https://toc.ui.ac.ir/article_3506_bfc02f2003611e70f89d3bbb16913cd1.pdf