Journal ArticleDOI
Wiener Index of Trees: Theory and Applications
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TLDR
The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph as discussed by the authors, defined as the distance between all vertices in a graph.Abstract:
The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph. The paper outlines the results known for W of trees: methods for computation of W and combinatorial expressions for W for various classes of trees, the isomorphism–discriminating power of W, connections between W and the center and centroid of a tree, as well as between W and the Laplacian eigenvalues, results on the Wiener indices of the line graphs of trees, on trees extremal w.r.t. W, and on integers which cannot be Wiener indices of trees. A few conjectures and open problems are mentioned, as well as the applications of W in chemistry, communication theory and elsewhere.read more
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Journal ArticleDOI
Wiener Index of Hexagonal Systems
TL;DR: In this paper, the authors present the results known for W of the HS: method for computing W, expressions relating W with the structure of the respective HS, results on HS's extremal w.r.t. W, and on integers that cannot be the W-values of HS's.
Journal ArticleDOI
Resistance distance and the normalized Laplacian spectrum
Haiyan Chen,Fuji Zhang +1 more
TL;DR: Not only is it shown the resistance distance can be naturally expressed in terms of the normalized Laplacian eigenvalues and eigenvectors of G, but also a new index which is closely related to the spectrum of the Normalized LaPLacian is introduced.
Book ChapterDOI
Chemical Graph Theory
Ernesto Estrada,Danail Bonchev +1 more
TL;DR: This chapter on chemical graph theory forms part of the natural science and processes section of the handbook.
Journal ArticleDOI
The first and second Zagreb indices of some graph operations
TL;DR: Some exact expressions for the first and second Zagreb indices of graph operations containing the Cartesian product, composition, join, disjunction and symmetric difference of graphs will be presented.
A Survey on Graphs Extremal with Respect to Distance-Based Topological Indices
TL;DR: In this article, the authors present a survey on graphs extremal with respect to distance-based indices, with emphasis on the Wiener index, hyper-Wiener index and the Harary index.
References
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Book ChapterDOI
A New Characterization of Tree Medians with Applications to Distributed Algorithms
Ori Gerstel,Shmuel Zaks +1 more
TL;DR: It is shown that, given a network of a tree topology, choosing a median and then routing all the information through it is the best possible strategy, in terms of worst-case number of messages sent during any execution of any distributed sorting algorithm.
Journal ArticleDOI
The Mean Isomer Degeneracy of the Wiener Index
TL;DR: In this paper, it was shown that there is a high isomer degeneracy in the case of molecules of medium size, namely when n = 6 and n = 7, where n is the number of vertices of the molecular graphs of the isomers considered.