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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The Wiener Polynomial of Polyomino Chains
TL;DR: In this paper, the Wiener polynomial of polyomino chains is defined, whose derivative is a x-analog of the original Wiener index, which is a graphical invariant and is the sum of distances between all pairs vertices in a connected graph.
Dissertation
Properties of graph polynomials and related parameters
TL;DR: Razanajatovo and Misanantenaina as discussed by the authors investigated various problems related to graph polynomials, including the average size of independent vertex sets of a graph, following the work of Jamison on subtrees.
Journal ArticleDOI
On the Edge Wiener Index
TL;DR: The edge Wiener index as discussed by the authors is defined as the sum of distances between all pairs of edges of a simple connected graph, where the distance between the edges f and g in E(G) in the line graph of G is defined by the distances between the vertices f and G in the vertex graph.
Topological Indices of Hypercubes
TL;DR: In this paper, the authors give explicit formulas for four topological indices (Wiener, Schultz, PI and Szeged) of hypercubes and their corresponding Euclidean graph.
Journal ArticleDOI
The Hosoya Polynomial of One-Pentagonal Carbon Nanocone
TL;DR: In this paper, the Hosoya polynomial of one-pentagonal carbon nanocone was derived for a series of distance-based molecular structure descriptors, such as the well-known Wiener index, the hyper-Wiener index and the Harary index.
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.