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 Hyper-Zagreb Index of Trees and Unicyclic Graphs
TL;DR: In this paper, the authors characterize the trees and unicyclic graphs with the first four and first eight greatest Hyper-Zagreb index values, respectively, and show that the trees have the highest HM-value.
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On the Wiener Index of Some Edge Deleted Graphs
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Schultz indices of F-sums graphs
TL;DR: In this article, the Schultz index of the F-sums graphs is calculated and the distance of two vertices u and v in the graph is computed for each vertex in the Euclidean space.
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Lower bound for the cost of connecting tree with given vertex degree sequence
TL;DR: The proposed lower bound estimate is used to construct several heuristic algorithms and to evaluate their quality on a variety of generated and real-life data sets.
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Computing zagreb indices and zagreb polynomials of fullerene, butterfly and benes networks
TL;DR: In this article, the hyper-Zagreb index, first multiple Zagreb, second multiple zagreb and relatedly the Zag Croatia polynomials were established in chemical graph theory by means of vertex degrees.
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.