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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Journal ArticleDOI
How to compute the Wiener index of a graph
Bojan Mohar,Tomaž Pisanski +1 more
TL;DR: In this article, an algorithm for computing the Wiener index of a tree in linear time is given. But it is not known whether the algorithm can be used to calculate the index of an arbitrary graph.
Journal ArticleDOI
The number of caterpillars
Frank Harary,Allen J. Schwenk +1 more
TL;DR: This neat formula is proved in two ways: first, as a special case of an application of Polya's enumeration theorem which counts graphs with integer-weighted points; secondly, by an appropriate labeling of the lines of the caterpillar.
Journal ArticleDOI
On the sum of all distances in composite graphs
Yeong-Nan Yeh,Ivan Gutman +1 more
TL;DR: The sum of distances between all pairs of vertices in these composite graphs is computed.
Journal ArticleDOI
Topological Indices Based on the Line Graph of the Molecular Graph
Ivan Gutman,Ernesto Estrada +1 more
TL;DR: The topological index e recently proposed by one of the authors is shown to be identical to the connectivity index of the line graph of the molecular graph, making it possible to conceive a whole class of novel, line-graph-based topological indices.
Journal ArticleDOI
The modeling of chemical phenomena using topological indices
TL;DR: A survey of the progress in this area and some of the advantages and drawbacks of using topological indices can be found in this paper, where the authors discuss the manifold applications of topological invariants to the description of physicochemical properties.