Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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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)
  • Received : 2012.10.17
  • Accepted : 2012.11.27
  • Published : 2013.05.30
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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.

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