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
Journal ArticleDOI
Note: A note on dominating sets and average distance
TL;DR: It is shown that the total domination number of a simple connected graph is greater than the average distance of the graph minus one-half, and that this inequality is best possible.
A Note on Wiener Index
TL;DR: In this paper, a lower bound for the Wiener index in terms of graph invariants is proposed, which is the same as the lower bound of the upper bound in this paper.
Journal ArticleDOI
Wiener Indices in Random Cyclooctane Chains
Shouliu Wei,Xiaoling Ke,Yan Wang +2 more
TL;DR: In this paper, simple exact formula are established for the expected value of Wiener index in random cyclooctane chain, and the average value of the Wiener indices with respect to the set of all cyclOOctane chains with n octagons.
Proceedings ArticleDOI
Labellings and invariants of models from complex networks
Bing Yao,Xiangqian Zhou,Jiajuan Zhang,Xiang'en Chen,Xiaoming Zhang,Jianming Xie,Ming Yao,Mogang Li +7 more
TL;DR: This work uses spanning trees to study some important characteristics of scale-free networks, and provides some connections between invariants of graphs in order to apply graph-theoretical methods to network problems.
Journal ArticleDOI
Degree-Based Topological Aspects of Polyphenylene Nanostructures
Yu-Ming Chu,Muhammad Numan,Saad Ihsan Butt,Muhammad Kamran Siddiqui,Rizwan Ullah,Murat Cancan,Usman Ali +6 more
TL;DR: In a molecular graph, molecules are associated with some numerical values these values are known as topological indices as discussed by the authors, from the M-polynomial of molecular structure we can derived degree-based topology indices.
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.