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
Citations
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Journal ArticleDOI
Distance-based topological indices of the tree-like polyphenyl systems
TL;DR: This paper investigates the relationships between the Wiener index and other distance-based topological indices in the tree-like polyphenyl systems and obtains some exactly formulae on the relationships.
Journal ArticleDOI
Statistical properties of linear-hyperbranched graft copolymers prepared via "hypergrafting" of AB(m) monomers from linear B-functional core chains: A molecular dynamics simulation.
TL;DR: The reaction of ABm monomers with a multifunctional Bf-type polymer chain ("hypergrafting") is studied by coarse-grained molecular dynamics simulations and Configurational chain properties are determined, showing that the stretching of the polymer backbone as a consequence of the "hypergrafted" procedure is much less pronounced than for perfectly dendronized chains.
Journal ArticleDOI
The Hyper-Wiener Index of One-pentagonal Carbon Nanocone
TL;DR: In this article, the hyper-Wiener index of one-pentagonal carbon nanocone has been calculated explicitly, which is the first attempt to calculate the hyper Wiener index explicitly.
Journal ArticleDOI
Maximal Wiener index for graphs with prescribed number of blocks
TL;DR: The sizes of a and b in the extremal graphs for each n and p are determined and unimodal property of a behaviour of Wiener index is showed.
Posted Content
Wiener index, number of subtrees, and tree eccentric sequence
TL;DR: In this paper, it was shown that the same tree maximises the number of subtrees among all trees with a given eccentric sequence, thus providing another example of negative correlation between the total number of trees and the Wiener index of 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.