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Wiener indices of trees and monocyclic graphs with given bipartition

✍ Scribed by Zhibin Du

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
155 KB
Volume
112
Category
Article
ISSN
0020-7608

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✦ Synopsis

Abstract

The Wiener index of a connected graph is defined as the sum of distances between all unordered pairs of its vertices. It has found various applications in chemical research. We determine the minimum and the maximum Wiener indices of trees with given bipartition and the minimum Wiener index of monocyclic graphs with given bipartition, respectively. We also characterize the graphs whose Wiener indices attain these values. Β© 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

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✍ Shuchao Li; Minjie Zhang πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 255 KB

For a (molecular) graph, the first Zagreb index M 1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M 2 is equal to the sum of products of the degrees of a pair of adjacent vertices. In this work, we study the Zagreb indices of bipartite graphs of order n with diame