RECIPROCAL DEGREE DISTANCE OF SOME GRAPH OPERATIONS

The reciprocal degree distance (rdd), dened for a connected graph g as vertex-degree-weighted sum of the reciprocal distances, that is, rdd(g) = p u;v2v (g)dg(u)+dg(v)dg(u;v) : the reciprocal degreedistance is a weight version of the harary index, just as the degree distance is a weight version of thewiener index. in this paper, we present exact formulae for the reciprocal degree distance of join, tensorproduct, strong product and wreath product of graphs in terms of other graph invariants including thedegree distance, harary index, the first zagreb index and first zagreb coindex. finally, we apply some ofour results to compute the reciprocal degree distance of fan graph, wheel graph, open fence and closedfence graphs.