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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On the neighbourhoods of trees
Peter J. Humphries,Taoyang Wu +1 more
TL;DR: An expression for the size of the TBR (tree bisection and reconnection) neighbourhood is presented, thus answering a question first posed in [Annals of Combinatorics, 5, 2001 1-15].
Journal ArticleDOI
COMPUTING WIENER INDEX OF HAC5C7[p, q] NANOTUBES BY GAP PROGRAM
Ali Iranmanesh,Yaser Alizadeh +1 more
TL;DR: An algorithm by GAP program is given that can be compute the Wiener index for any graph; also theWiener index of HAC5C7(p,q) and Hac5C6C7 (p, q) nanotubes is computed by this program.
Book ChapterDOI
On a conjecture on Wiener indices in combinatorial chemistry
TL;DR: This paper presents a 4-parameter family of trees that are shown experimentally to affirm the Wiener index conjecture for very large values of n, and presents efficient algorithms for finding the tree whoseWiener index is n.
Journal ArticleDOI
On the eccentric subtree number in trees
TL;DR: The eccentric subtree number at a vertex v in T is studied, defined as η T e c c ( v ) = min u ∈ V ( T )η T ( v, u ) .
Posted Content
On Wiener polarity index of cactus graphs
Nan Chen,Wen-Xue Du,Yi-Zheng Fan +2 more
TL;DR: In this article, the authors give an explicit formula for the Wiener polarity index of cactus graphs, and also deduce formulas for some special cactus graph types, such as cactus 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.