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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Anomalous behavior of trapping in extended dendrimers with a perfect trap
Zhongzhi Zhang,Huan Li,Yuhao Yi +2 more
TL;DR: It is shown that the trap location has a substantial influence on the trapping efficiency measured by the ATT, which increases with the shortest distance from the trap to the central node, a phenomenon similar to that for compact dendrimers.
Journal ArticleDOI
On Molecular Descriptors of Face-Centered Cubic Lattice
TL;DR: In this article, a topological index of a molecular graph G is a numeric amount identified with G, which depicts its topological properties, and the molecular descriptors (topological indices) are computed using graph theory tools.
Journal ArticleDOI
A Method for Computing the Wiener Index of One-Pentagonal Carbon Nanocones
Journal ArticleDOI
Second Zagreb indices of transformation graphs and total transformation graphs
TL;DR: In this article, the second Zagreb index of semitotal-line graph, semiotal-point graph, and total transformation graph Gxyz was given explicit formulas.
The edge versions of the
TL;DR: In this paper, the edge-Wiener index is defined as the sum of distances between all pairs of edges of the underlying (connected) graph, and several possible distances between edges of a graph are considered and, according to these, the corresponding edgeWiener indices defined.
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.