Journal ArticleDOI
Wiener Index of Trees: Theory and Applications
Reads0
Chats0
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
More filters
Relation between wiener index and spectral radius
TL;DR: In this article, the relation between the Wiener index W and spectral radius λ 1 has been compared and it has been shown that within series of the isomeric chemical trees there exists a decreasing linear correlation between W and λ1.
Journal ArticleDOI
Relations between Wiener, hyper-Wiener and some Zagreb type indices
TL;DR: In this paper, some inequalities between the Wiener, hyper-Wiener, first Zagreb, second Zagrebe, first reformulated Zagrec, and the general ZAGreb indices of a simple graph are given.
Proceedings ArticleDOI
Leaves and inverse degree of a graph
TL;DR: For a tree T on n vertices, 2 ≤ 2 · id(T ) - n ≤ n 1 (T), diam(T) + n 1(T + 1 ≤ 2 ǫ · id (T), and 2 ·id(T)-n 1 (t)−1 over 2n 2 (T)+1 for a largest matching M of T.
Journal ArticleDOI
Computing Irregularity Indices for Probabilistic Neural Network
TL;DR: This paper discusses thirteen irregularity indices for probabilistic neural networks (PNN) and their most critical use to date is in Neurochemistry.
Journal ArticleDOI
On topological properties of block shift and hierarchical hypercube networks
TL;DR: Analytical closed results of hyper Zagreb index, first multiple Zag Croatia index, second multiple Zgere index, ZagCro polynomials and redefined Zagre indices for block shift network and hierarchical hypercube are derived.
References
More filters
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.