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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Proceedings Article
A topological approach to real networks.
Silvana Stefani,Anna Torriero +1 more
TL;DR: En Topological structures of real networks are investigated using some relevant descriptive indicators suitable for specific applicative contexts.
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On the cozero-divisor graphs associated to rings
TL;DR: In this paper, the Laplacian spectral radius and algebraic connectivity of a cozero-divisor graph of a ring with unity were studied. And the Wiener index of the graph was characterized for any constant n = p ∈ {n, q, n, q} where n is the number of vertices in the graph.
Journal ArticleDOI
The reciprocal complementary Wiener number of graphs
TL;DR: The reciprocal complementary Wiener number (RCW) of a connected graph G is defined as the sum of weights frac{1}{D+1-d_G(x,y)} over all unordered vertex pairs in a graph G, where D is the diameter of the vertices and G is the distance between vertices x and y.
Journal ArticleDOI
On Degree-Based Topological Indices of Thermodynamic Cuboctahedral Bi-Metallic Structure
TL;DR: In this article , the first and second Zagrebar index, the augmented zagreb index, and the inverse Randic, as well as general Randic index, symmetric division, and harmonic index were calculated.
Journal ArticleDOI
Topological Characterization of the Crystallographic Structure of Titanium Difluoride and Copper (I) Oxide
TL;DR: In this article, the authors determined a hyper-Zagreb list, a first multiple Zagreb file, a second different Zag Croatia record and polynomials for titanium difluoride (TiF2) and the crystallographic structure of Cu2O.
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.