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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Computing the Wiener Index of a TUC4C8(S) Nanotorus
Ali Reza Ashrafi,Shahram Yousefi +1 more
TL;DR: In this article, an algorithm for computing the distance matrix of a TUC4C8(R) nanotorus T = T[m,n] is given, using this matrix, the following expression for the Wiener index of T is obtained,
Journal ArticleDOI
Generalizations of Wiener Polarity Index and Terminal Wiener Index
Aleksandar Ilic,Milovan Ilic +1 more
TL;DR: In this paper, a generalized Wiener polarity index W k (G) was introduced for trees and partial cubes, and a linear time algorithm for computing these indices was described.
Journal ArticleDOI
New composition of graphs and their Wiener Indices
TL;DR: In this paper, the authors define new graph operations F-composition F (G)[H], where F(G) is one of the symbols S(G),M(G,Q,T,G),Λ(G],Λ[G],D2(G]),D2[G].
Journal ArticleDOI
On maximum Wiener index of trees and graphs with given radius
TL;DR: An upper bound on Wiener index of trees and graphs in terms of number of vertices n, radius r, and maximum degree is given and the extremal graphs are characterized.
Posted Content
Hitting Times, Cover Cost, and the Wiener Index of a Tree
TL;DR: In this paper, a connection between hitting times of the simple random walk on a graph, the Wiener index, and related graph invariants is made. But the connection is not restricted to trees.
References
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Journal ArticleDOI
Laplacian matrices of graphs: a survey
TL;DR: In this paper, the authors survey some of the many results known for Laplacian matrices, and present a survey of the most important results in the field of graph analysis.
THE LAPLACIAN SPECTRUM OF GRAPHS y
TL;DR: A survey of known results about the spectrum of the Laplacian matrix of graphs with special emphasis on the second smallest Lapla-cian eigenvalue 2 and its relation to numerous graph invariants, including connectivity, expanding properties, isoperimetric number, maximum cut, independence number, genus, diameter, mean distance, and bandwidth-type parameters of a graph is given in this article.
Book
Mathematical concepts in organic chemistry
Ivan Gutman,Oskar E. Polansky +1 more
TL;DR: In this paper, the authors define the topology of a graph as follows: 1.1 Topology in Chemistry, 2.2 Geometry, Symmetry, Topology, Graph Automorphisms, and Graph Topology.