Pattabiraman, K., Vijayaragavan, M. (2013). Reciprocal degree distance of some graph operations. Transactions on Combinatorics, 2(4), 13-24. doi: 10.22108/toc.2013.3506

Kannan Pattabiraman; M. Vijayaragavan. "Reciprocal degree distance of some graph operations". Transactions on Combinatorics, 2, 4, 2013, 13-24. doi: 10.22108/toc.2013.3506

Pattabiraman, K., Vijayaragavan, M. (2013). 'Reciprocal degree distance of some graph operations', Transactions on Combinatorics, 2(4), pp. 13-24. doi: 10.22108/toc.2013.3506

Pattabiraman, K., Vijayaragavan, M. Reciprocal degree distance of some graph operations. Transactions on Combinatorics, 2013; 2(4): 13-24. doi: 10.22108/toc.2013.3506

Reciprocal degree distance of some graph operations

^{2}Thiruvalluvar College of Engineering and Technology

Abstract

The reciprocal degree distance (RDD), defined for a connected graph $G$ as vertex-degree-weighted sum of the reciprocal distances, that is, $RDD(G) =\sum\limits_{u,v\in V(G)}\frac{d_G(u) + d_G(v)}{d_G(u,v)}.$ 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.

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