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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Journal ArticleDOI
On the extremal graphs of diameter 2 with respect to the eccentric resistance-distance sum
TL;DR: The graphs of diameter 2 with the largest, second largest, third largest, smallest, second smallest and third smallest eccentric resistance-distance sums are identified, respectively.
Journal ArticleDOI
On distances in vertex-weighted trees
TL;DR: The behavior of vertex-weighted distance sum in general is analyzed, identifying the “middle part” of a tree analogous to that with respect to the regular distance sum, and a simpler approach is provided to obtain a stronger result regarding the extremal tree with a given degree sequence.
Chemical Graphs Constructed of Composite Graphs and Their q-Wiener Index
Ali Iranmanesh,Ivan Gutman +1 more
TL;DR: In this paper, the q-analog of W, motivated by the theory of hypergeometric series, has been derived for the q -Wiener index of cluster and corona of graphs, of which thorny and bridge graphs are special cases.
Journal ArticleDOI
Computing Banhatti Indices of Hexagonal, Honeycomb and Derived Networks
TL;DR: The general and modified K Banhatti indices for hexagonal, honeycomb and honeycomb derived networks are computed.
Journal ArticleDOI
Algorithms Based on Path Contraction Carrying Weights for Enumerating Subtrees of Tricyclic Graphs
TL;DR: This approach provides a foundation and useful methods to compute subtree number index for graphs with more complicated cycle structures and can be applied to investigate the novel structural property of some important nanomaterials such as the pentagonal carbon nanocone.
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.