Journal ArticleDOI
Wiener Index of Trees: Theory and Applications
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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
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Computing Szeged Index of Certain Nanosheets Using Partition Technique
TL;DR: The Szeged index as discussed by the authors is a molecular structure descriptor equal to the sum of products over all edges of the molecular graph G, where neu(e|G )i s the number of vertices whose distance to vertex u is smaller than the distance u to vertex v,a nd wherenev(e |G) is defined analogously.
Journal ArticleDOI
On Topological Indices of Certain Families of Nanostar Dendrimers
TL;DR: The fourth version of ABC index and the fifth version of GA index of certain families of nanostar dendrimers are investigated and the analytical closed formulas for these families are derived.
Journal ArticleDOI
Stochastically evolving networks.
TL;DR: A class of models for the evolution of networks in which new nodes are recruited into the network atrandom times, and links between existing nodes that are not yet directly connected may also form at random times is discussed.
Trees with extremal Wiener indices
S. J. Wang,X. F. Guo,郭晓峰 +2 more
TL;DR: In this paper, the authors considered the trees with order n, diameter d or maximum degree and extremal Wiener indices, and obtained the tree with minimum Wiener index among all the trees of order n and with diameter d.
Journal ArticleDOI
Trees with the seven smallest and eight greatest Harary indices
TL;DR: This paper has determined the first up to seventh smallest Harary indices of trees of order n>=16 and the firstUp to eighth greatest Harary index of treesof order n=14.
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.