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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The Kirchhoff indices and the matching numbers of unicyclic graphs
TL;DR: The minimum Kirchhoff index of a connected graph is the sum of resistance distances between all unordered pairs of vertices in the graph as discussed by the authors, which is defined as a measure of the distance between two vertices.
Journal Article
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.
Posted Content
Rearranging trees for robust consensus
TL;DR: This paper restricts attention to trees, and by systematic attention to the effect of local changes in topology, derives a partial ordering for undirected trees according to the ℋ2 norm, which provides a constructive method for deriving an ordering for directed trees.
Journal ArticleDOI
Extremal values on Zagreb indices of trees with given distance k -domination number
Lidan Pei,Xiang-Feng Pan +1 more
TL;DR: The upper bounds for the Zagreb indices of n-vertex trees with given distance k-domination number are obtained and the extremal trees are characterized, which generalize the results of Borovićanin and Furtula.
Journal ArticleDOI
The Wiener Index of r -Uniform Hypergraphs
TL;DR: The concept of the chemical bond-Wiener index of a graph was introduced in this paper, which is the sum of the distances between all pairs of chemical bonds in a graph, considering the removal of hydrogen atoms.
References
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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.