Journal ArticleDOI
Wiener Index of Trees: Theory and Applications
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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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The Terminal Wiener Index of Trees with Diameter or Maximum Degree
Ya-Hong Chen,Xiao-Dong Zhang +1 more
TL;DR: In this paper, the authors presented a sharp upper and lower bound for the terminal Wiener index in terms of its order and diameter and characterised all extremal trees which attain these bounds.
Journal ArticleDOI
The multiplicative version of wiener index
Hongbo Hua,Ali Reza Ashrafi +1 more
TL;DR: The multiplicative version of Wiener index (index) is equal to the product of the distances between all pairs of vertices of a (molecular) graph G as mentioned in this paper.
Journal ArticleDOI
On Some Banhatti Indices of Triangular Silicate, Triangular Oxide, Rhombus Silicate and Rhombus Oxide Networks
TL;DR: In this paper, the general K-Banhatti index, first and second K-banhatti indices, K hyper Banhatti Index and modified K Banhattii indices for triangular silicate network, triangular oxide network, rhombus oxide network and rhombous silicate networks are computed.
Journal ArticleDOI
q-Wiener index of some compound trees
TL;DR: In this article, formulas are obtained for computing the q-Wiener indices of some compound trees, and these generalize expressions, earlier known to hold for W. The q-analogs of W were conceived, motivated by the theory of hypergeometric series.
Book ChapterDOI
Complexity of splits reconstruction for low-degree trees
TL;DR: This work considers the problem of constructing a tree on V whose splits correspond to S, and shows that the problem is strongly NP-complete when T is required to be a path, and the problem when the vertex weights are not given but can be freely chosen by an algorithm.
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.