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
Citations
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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
A novel definition of the Wiener index for trees
Journal ArticleDOI
A Collective Property of Trees and Chemical Trees
Mirko Lepović,Ivan Gutman +1 more
TL;DR: The Wiener index (W) and the Hosoya polynomial (H) has been calculated and it is shown that the ability of W to distinguish between nonisomorphic n-vertex trees depends on n in an alternating manner: it increases for evenvalues of n and decreases for odd values of n.
Journal ArticleDOI
Extension of Edge Connectivity Index. Relationships to Line Graph Indices and QSPR Applications
TL;DR: The study of eight representative physical properties of alkanes was used to compare the ability of both series of indices to produce significant quantitative structure−property relationship (QSPR) models.
Journal ArticleDOI
Determination of the Wiener molecular branching index for the general tree
TL;DR: In this paper, a general recursion formula for trees of any kind is presented, which is valid irrespective of the valence of the vertices of the tree or the degree of branching in the tree.
Journal ArticleDOI
Trees with Extremal Hyper-Wiener Index: Mathematical Basis and Chemical Applications
TL;DR: Trees with minimal and maximal hyper-Wiener indices (WW) are determined among n-vertex trees, minimum and maximum WW is achieved for the star-graph and the path-graph, respectively.