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
Topological indices of the bipartite Kneser graph Hn,k
R. Mohammadyari,M.R. Darafsheh +1 more
TL;DR: In this paper, the authors used transitivity property of the automorphism group of the bipartite Kneser graph to calculate its Wiener, Szeged and PI indices.
Proceedings ArticleDOI
Wiener odd and even indices on BC-Trees
TL;DR: It is theoretically that Wiener odd index is not more than its even index for general BC-Trees and closed formulae of the two indices are provided for path BC-tree, star, k-extending star tree and caterpillar BC- tree.
Journal ArticleDOI
On the extremal graphs with respect to the total reciprocal edge-eccentricity
TL;DR: This paper first characterize the unique graph with the maximum total reciprocal edge-eccentricity among all graphs with a given number of cut vertices, and determines the k -connected bipartite graphs of order n with diameter d having themaximum total reciprocal edges.
A note on topological indices and the twin classes of graphs
TL;DR: In this paper , it was shown that computing the Steiner Wiener index of a graph can be reduced to the same for a much smaller graph, called the reduced graph of the graph.
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.