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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Journal ArticleDOI
The hyper edge-Wiener index of corona product of graphs
TL;DR: In this paper, the authors presented explicit formula for the hyper edge-Wiener index of corona product of two graphs. And they used it to determine the hyper-edge Wiener index for some chemical graphs.
Journal ArticleDOI
Irregularity indices for line graph of Dutch windmill graph
Mohanad A. Mohammed,Suad Younus A. AL-Mayyahi AL-Mayyahi,Abaid ur Rehman Virk,Hafiz Mutee ur Rehman +3 more
TL;DR: In this article, some irregularity indices that are useful in quantitative structure activity relationship for Line Graph of Dutch Windmill graph are computed. But they have a conspicuous role in chemistry.
Journal ArticleDOI
On the k-ary hypercube tree and its average distance
TL;DR: The d-dimensional k-aryhypercube tree T k (d) is a generalization of the hypercube tree, also known in the literature as the spanning binomial tree and it is shown that its total distance is , which is minimum.
Proceedings ArticleDOI
Some results on Wiener index of a graph: an overview
TL;DR: The only known graph with this property is the cycle C11 as mentioned in this paper, which is the only known connected graph for which the Wiener index does not change when a particular vertex v is removed.
Journal ArticleDOI
Ordering the non-starlike trees with large reverse wiener indices
Shuxian Li,Bo Zhou +1 more
TL;DR: In this article, the reverse Wiener index of a connected graph G is defined as the sum of distances between all unordered pairs of vertices of G, where G is the number of nodes, d is the diameter, and W(G) is the 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.