Journal ArticleDOI
Wiener Index of Trees: Theory and Applications
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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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Book ChapterDOI
Equiseparability on Terminal Wiener Index
Xiaotie Deng,Jie Zhang +1 more
TL;DR: The properties of terminal Wiener index are explored, and the fact that there still exist pairs of trees and chemical trees which can not be distinguished by it is shown, to show that terminalWiener index is degenerative to some extent.
Journal ArticleDOI
The Wiener index of the zero-divisor graph of a finite commutative ring with unity
TL;DR: In this article , the authors derived a formula for the Wiener index of the zero-divisor graph Γ (R ) for R = Z n , the ring of integers modulo n.
Wiener index of generalized 4-stars and of their quadratic line graphs.
Martin Knor,Riste Škrekovski +1 more
TL;DR: Several infinite families of trees are constructed which have a unique branching vertex of degree 4 and whose Wiener index equals theWiener index of their quadratic line graph.
Journal ArticleDOI
Wiener index of certain families of hexagonal chains
Andrey A. Dobrynin,Ehsan Estaji +1 more
TL;DR: The Wiener index as discussed by the authors is a topological index of a molecule defined as the sum of distances between all pairs of vertices in the chemical graph representing the non-hydrogen atoms in the molecule.
Journal ArticleDOI
The Wiener index of unicyclic graphs given number of pendant vertices or cut vertices
TL;DR: In this article, the authors gave a condition to determine the graphs having the smallest Wiener index among all unicyclic graphs given number of pendant vertices, and also determined the graph with the smallest cut vertices.
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.