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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On Szeged‐type indices of titanium oxide TiO2 nanotubes
Journal ArticleDOI
On σ-span and F-span of trees and full binary trees
TL;DR: The difference between the values of σ T ( v ) at a centroid vertex and a leaf, called the σ -span, and similarly the F -span for the difference in values of the local subtree index at the subtree core and at a leaf are studied.
Journal Article
Ashwini Index of a Graph
TL;DR: In this paper, the authors defined the Ashwini index of trees as the distance between the vertices of the shortest path starting at a node and ending at another node in a tree.
Journal ArticleDOI
Proof of a conjecture on the Wiener index of Eulerian graphs
TL;DR: In this paper, the authors proved that the cycle is the unique graph maximising the Wiener index among all Eulerian graphs of given order, and they also conjectured that for Eulerians of order n ≥ 26, the graph consisting of a cycle on n − 2 vertices and a triangle that share a vertex is the one with the second largest Wiener Index.
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Remarks on Distance Based Topological Indices for ℓ-Apex Trees
TL;DR: In this article, extremal values of several monotonic distance-based topological indices for this class of graphs, namely generalized Wiener index and the Harary index, and also for some newer indices as connective eccentricity index, generalized degree distance, and others.
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.