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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Computing the degree based topological indices of line graph of benzene ring embedded in P-type-surface in 2D network
TL;DR: In this article, a topological index for a graph is defined, where a solitary number that can be used to describe some property of the graph of a particle is known as a topology index for that graph.
Relations between Zagreb Coindices and Some Distance-Based Topological Indices ∗
Hongbo Hua,Shenggui Zhang +1 more
TL;DR: In this article, the first Zagreb coindex is defined as the sum of degree sum over all non-adjacent vertex pairs in G and the second Zagrabox coindex, which measures the degree product over all vertices in G. The relation between the first coindex and distance-based topological indices is investigated.
Journal ArticleDOI
FibVID: Comprehensive fake news diffusion dataset during the COVID-19 period
TL;DR: A valuable dataset called FibVID (Fake news information-broadcasting dataset of CO VID-19), which addresses COVID-19 and non-COVID news from three key angles and helps to uncover propagation patterns of news items and themes related to identifying their authenticity.
Journal ArticleDOI
Extremal polyomino chains with respect to Zagreb indices
TL;DR: Zagreb indices of polyomino chains are computed and the extremal polyominos chains with respect to Zag Croatia indices are determined.
Posted Content
Distance spectra and Distance energy of Integral Circulant Graphs
TL;DR: In this paper, the authors characterized the distance spectra of integral circulant graphs and proved that these graphs have integral eigenvalues of distance matrix (D) and showed that they can be represented as unitary Cayley graphs.
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.