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 indices of Wiener and anti-Wiener type
Damir Vukičević,Jelena Sedlar +1 more
TL;DR: The introduced order of tree graphs has the star S n for minimal graph, while the path P n is the maximal graph, so that all indices of Wiener type obtain minimum value for S n and maximum value for P n , while the reverse holds for indices of anti-Wiener type.
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The Wiener Index of Unicyclic Graphs with Girth and the Matching Number
Ya-Hong Chen,Xiao-Dong Zhang +1 more
TL;DR: A sharp lower bound is presented for the Wiener index of unicyclic graphs of order n with girth and the matching number � � 3g 2 .
Journal ArticleDOI
The study of an infinite class of dendrimer nanostars by topological index approaches
Ali Reza Ashrafi,Mahsa Mirzargar +1 more
TL;DR: In this article, an infinite class of dendrimer nanostars is investigated under three topological indices, namely PI, Szeged and edge szeged, and it is shown that PI is invariant under automorphisms of a molecular graph.
Journal Article
Computing the Hosoya Polynomial, Wiener Index and Hyper-Wiener Index of the Harary Graph
TL;DR: In this paper, the Hosoya polynomial of the Harary graph was computed and the Wiener index and the hyper-Wiener index of the regular Harary graphs were computed.
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.