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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Journal ArticleDOI
The Steiner Wiener Index of A Graph
TL;DR: The Steiner k-Wiener index SWk(G) of G is defined by .
Algorithm sa nd Extre mal Problem on Wiener Polarity Index
TL;DR: This paper describes a linear time algorithm APT for computing the index of trees, and describes the trees maximizing the index among all trees of given order.
Journal ArticleDOI
A matrix method for computing Szeged and vertex PI indices of join and composition of graphs
TL;DR: The Szeged index as mentioned in this paper extends the Wiener index for cyclic graphs by counting the number of vertices on both sides of each edge and sum these counts, which can be used for join and composition of graphs.
Journal ArticleDOI
Wiener index in weighted graphs via unification of Θ*-classes
TL;DR: It is proved that the Wiener index of a weighted graph (G,w) can be expressed as the sum of theWiener indices of weighted quotient graphs with respect to an arbitrary combination of @Q^*-classes.
The Wiener index of a graph
TL;DR: In this article, the authors declare that they have authored this thesis independently, that I have not used other than the declared sources/resources, and that they explicitly marked all material which has been quoted either literally or by content from the used sources.
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.