reciprocal degree distance of some graph operations

نویسندگان

kannan pattabiraman

m. vijayaragavan

چکیده

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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عنوان ژورنال:
transactions on combinatorics

ناشر: university of isfahan

ISSN 2251-8657

دوره 2

شماره 4 2013

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