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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The HyperZagreb Index of Graph Operations
TL;DR: In this article, the first and second Zagreb indices have been introduced and a simple connected graph G is defined, where G is a simple graph and G is connected by vertices.
Journal ArticleDOI
Computing topological indices of chemical structures of the conductive 2D MOFs
TL;DR: Degree based topological indices of chemical structures of the conductive 2D MOFs Cu 3(HITP)2[m, n] are studied in this paper. But they do not consider the properties of the MOFs.
Journal ArticleDOI
On investigations of graphs preserving the Wiener index upon vertex removal
TL;DR: In this article, it was shown that there are infinitely many graphs such that the Wiener index of a graph G = W(G - \{v_1, \ldots, v_r\}) can be computed in such a way that the vertices of G are distinct vertices.
Differences between detour and Wiener indices
Modjtaba Ghorbani,Nasrin Azimi +1 more
TL;DR: It is shown that for any positive integer n �, 2, 4, 6 there is a graph with µ(G )= n and Nadjafi-Arani et al.'s work to prove this.
Journal ArticleDOI
Extremal properties of reciprocal complementary Wiener number of trees
TL;DR: This work characterize the trees of fixed number of vertices and matching number with the smallest RCW number, and the trees that are not caterpillars on n ≥ 7 vertices with the largest, the smallest and the third-smallest RCW numbers.
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.