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
The Wiener, the hyper-Wiener and the degree distance indices of the bar polyhex graph
TL;DR: In this article, Kordala, El Marraki, Mohamed El-Marraki and Mohamed Essalih gave some theoretical results of the Wiener index W (Gp) and the 8772 Ayoub Kordalla, Mohamed el Marraaki and MohamedEssalih Hyper-Wiener index WW (GP) for a bar polyhex graph withe p hexagons Gp, using dGp(k), the number of pairs of vertices of Gp that have the same distance k ), and the diameter of GP.
Disturbance Propagation in Interconnected Linear Dynamical Networks
TL;DR: Several existing performance measures in real–world applications, such as total power loss in sync hronous power networks and flock energy of a group of autonomous vehicles in a formation, are indeed spec ial forms of Laplacian energies.
Proceedings ArticleDOI
Computing the Wiener index in Sierpiński carpet graphs
TL;DR: In this paper, an algorithm to compute the Wiener index of a sequence of finite graphs approximating the Sierpinski carpet is described, and the algorithm is shown to be efficient.
Journal ArticleDOI
On the Wiener Indices of Trees Ordering by Diameter-Growing Transformation Relative to the Pendent Edges
TL;DR: In this article, a graph transformation named diameter-growing transformation relative to pendent edges, which increases the Wiener index of a tree sharply after finite steps, was proposed and twenty-two trees were ordered by their Wiener indices.
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.