reciprocal degree distance of some graph operations
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abstract
the reciprocal degree distance (rdd), defined for a connected graph $g$ as vertex-degree-weighted sum of the reciprocal distances, that is, $rdd(g) =sumlimits_{u,vin v(g)}frac{d_g(u) + d_g(v)}{d_g(u,v)}.$ 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.
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Journal title:
transactions on combinatoricsPublisher: university of isfahan
ISSN 2251-8657
volume 2
issue 4 2013
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