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http://dx.doi.org/10.14317/jami.2013.533

THE MULTIPLICATIVE VERSION OF WIENER INDEX  

Hua, Hongbo (Department of Applied Mathematics, Northwestern Polytechnical University)
Ashrafi, Ali Reza (Department of Mathematics, Faculty of mathematical Sciences, University of Kashan)
Publication Information
Journal of applied mathematics & informatics / v.31, no.3_4, 2013 , pp. 533-544 More about this Journal
Abstract
The multiplicative version of Wiener index (${\pi}$-index), proposed by Gutman et al. in 2000, is equal to the product of the distances between all pairs of vertices of a (molecular) graph G. In this paper, we first present some sharp bounds in terms of the order and other graph parameters including the diameter, degree sequence, Zagreb indices, Zagreb coindices, eccentric connectivity index and Merrifield-Simmons index for ${\pi}$-index of general connected graphs and trees, as well as a Nordhaus-Gaddum-type bound for ${\pi}$-index of connected triangle-free graphs. Then we study the behavior of ${\pi}$-index upon the case when removing a vertex or an edge from the underlying graph. Finally, we investigate the extremal properties of ${\pi}$-index within the set of trees and unicyclic graphs.
Keywords
Distance; Wiener index; multiplicative Wiener index; bounds; extremal graphs;
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