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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Proceedings ArticleDOI
Constructing Influence Trees from Temporal Sequence of Retweets: An Analytical Approach
TL;DR: This paper develops CasCon, an unsupervised model that leverages on temporal pattern of retweets obtained from time series of cascades and underlying follower network of Twitter to construct influence trees, and provides an analytical formulation of CasCon that is validated on the influence tree structures of both synthetic and real cascades.
Dissertation
Asymptotiques de fonctionnelles d'arbres aléatoires et de graphes denses aléatoires
TL;DR: In this article, the authors propose a set of fonctionnelles additive for the convergence of graphs in the Galton-Watson condition, i.e. the convergence between two sets of graphs, simples and densites.
Journal ArticleDOI
Nordhaus-Gaddum-type inequality for the hyper-Wiener index of graphs when decomposing into three parts
TL;DR: This paper investigates the Nordhaus-Gaddum-type inequality of a 3-decomposition of K"n for the hyper-Wiener index: 7n2@?WW(G"1)+WW (G"2)+WW( G"3)@?2n+24+n2+4(n-1). the corresponding extremal graphs are characterized.
Journal ArticleDOI
On the Eccentric-Connectivity Index of Some 3-Fence Graphs and Their Line Graphs
Mehar Ali Malik,Rashid Farooq +1 more
TL;DR: In this paper, the authors considered infinite families of 3-fence graphs namely ladder, circular ladder and Mobius ladders and computed the eccentricity based topological indices of these graphs and their line graphs.
Journal ArticleDOI
On detour index of cycloparaphenylene and polyphenylene molecular structures.
TL;DR: In this paper, the authors present an exact analytical expression for the detour index of cycloparaphenylene and poly (para-phenylene) with respect to a two-dimensional methodology.
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.