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
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On hyper-Kirchhoff index
Rundan Xing,Bo Zhou +1 more
TL;DR: Lower and upper bounds for the hyper-Kirchhoff index are given, and the n -vertex unicyclic graphs with the smallest, the second and the third smallest as well as the largest are determined.
Posted Content
The weighted vertex PI index
TL;DR: The vertex PI index is a distance-based molecular structure descriptor that recently found numerous chemical applications as discussed by the authors, and the weighted version defined as $PI_w (G) was introduced to increase diversity of this topological index for bipartite graphs.
Journal ArticleDOI
Hosoya polynomials of random benzenoid chains
TL;DR: In this article, the expected value of the Hosoya polynomial of a random benzenoid chain with n hexagons was analyzed. But the expected values of the well-known topological indices: Wiener index, hyper-Wiener index and TratchStankevitchZefirov index were not analyzed.
Sparse Trees with a Given Degree Sequence
TL;DR: Wang et al. as discussed by the authors proposed the Steiner Wiener index of trees, which measures the distance between two vertices of a tree. But the index does not capture the properties of the vertices.
Journal ArticleDOI
Wiener invariants of product of graphs
S. Nagarajan,G. Priyadharsini +1 more
TL;DR: A topological descriptor is a numerical descriptor of a molecule based on a certain topological feature of the corresponding molecular graph as discussed by the authors, which is a representation of an object giving information only about the number of elements composing it and their connectivity.
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.