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On the reformulated reciprocal degree distance of graphs


K. PATTABIRAMAN, M. VIJAYARAGAVAN


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abs_cmi_2016_25_2_205-213

The reciprocal degree distance (RDD), defined for a connected graph G as vertex-degree-weighted sum of the reciprocal distances, that is, RDD(G) = P u,v∈V (G) (d(u)+d(v)) dG(u,v) . The new graph invariant named reformulated reciprocal degree distance is defined for a connected graph G as Rt(G) = P u,v∈V (G) (d(u)+d(v)) dG(u,v)+t , t ≥ 0. The reformulated reciprocal degree distance is a weight version of the t-Harary index, that is, Ht(G) = P u,v∈V (G) 1 dG(u,v)+t , t ≥ 0. In this paper, the reformulated reciprocal degree distance and reciprocal degree distance of disjunction, symmetric difference, Cartesian product of two graphs are obtained. Finally, we obtain the reformulated reciprocal degree distance and reciprocal degree distance of double a graph.