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 PI and Edge Szeged Indices of One-Heptagonal Carbon Nanocones
TL;DR: In this article, the Padmakar-Ivan (PI) and edge Szeged indices of one-heptagonal carbon nanocone CNC7(n) were computed for the first time.
Journal ArticleDOI
Some remarks on inverse Wiener index problem
TL;DR: An algorithm with a constant number of operations to construct a tree with a given Wiener index is presented and it is shown that there exist 2^@W^(^w^4^) non-isomorphic trees with WienerIndex w.
Journal ArticleDOI
Distance and eccentricity based invariants of windmill graph
TL;DR: In the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index also known as a connectivity index is a type of a molecular descriptor that is ca...
Journal ArticleDOI
Wiener Index of Graphs with Radius Two
TL;DR: The maximum Wiener index of a graph is the sum of the distances between all pairs of vertices as discussed by the authors, and it has been one of the main descriptors that correlate a chemical compound's molecular graph with experimentally gathered data regarding the compound's characteristics.
Journal ArticleDOI
The Terminal Hosoya Polynomial of Some Families of Composite Graphs
TL;DR: In this paper, the authors obtained closed formulae for the terminal Hosoya polynomial of rooted product graphs and corona product graphs with respect to the set of pendent vertices of a connected graph.
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.