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
A sharp lower bound on Steiner Wiener index for trees with given diameter
TL;DR: Using some transformations, a sharp lower bound is got on Steiner k -Wiener index for trees with given diameter, and the corresponding extremal graph is obtained as well.
Journal ArticleDOI
On the coefficients of the laplacian characteristic polynomial of trees
Ivan Gutman,Ljiljana Pavlović +1 more
TL;DR: In this article, the Laplacian characteristic polynomial of an n-vertex tree T was shown to be polynomially equivalent to the path and the star in the tree.
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Wiener index for graphs and their line graphs with arbitrary large cyclomatic numbers
TL;DR: Infinite families of graphs with increasing cyclomatic number and the property W ( G) = W ( L ( G ) ) are presented and this gives a positive (partial) answer to an open question.
Journal ArticleDOI
Comparison between the Szeged index and the eccentric connectivity index
TL;DR: A lower bound on S z - ?
Journal ArticleDOI
An exact expression for the wiener index of a TUC4C8(R) nanotorus
Shahram Yousefi,Ali Reza Ashrafi +1 more
TL;DR: In this paper, an algorithm for computing the distance matrix of a CSpaceEngineers 4>>\s Cーテ 8(R) nanotorus T ǫ = T[p,q] is given.
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.