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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Counting the numbers of paths of all lengths in dendrimers and its applications
TL;DR: In this paper , for any positive integer l, the average distance of Tn,k has been shown to be upper bounded by the number of paths of length l of the dendrimer.
Journal ArticleDOI
Extremal bipartite graphs and unicyclic graphs with respect to the eccentric resistance-distance sum
Shuchao Li,Changlong Shen +1 more
TL;DR: Among the bipartite graphs of diameter 2 and 3, the smallest and second smallest eccentric resistance-distance sums are characterized in this article, respectively, and the graphs with given girth are identified.
Proceedings ArticleDOI
The Relative Extrema of Vertex Degree Distances of Dumbbell Graphs
TL;DR: In this article , the vertex degree distances of the dumbbell graph and the distribution of the relative extrema of vertex degree distance on the path and on two cycles of the smart-bell graph are studied.
Journal ArticleDOI
On Subtree Number Index of Generalized Book Graphs, Fan Graphs, and Wheel Graphs
TL;DR: In this article, the authors presented the subtree generating functions and subtree number index of generalized book graphs, generalized fan graphs, and generalized wheel graphs, respectively, and provided the basis for studying novel structural properties of the graphs generated by these three types of graphs from the perspective of the sub-tree number index.
Posted Content
Reverse degree distance of unicyclic graphs
Zhibin Du,Bo Zhou +1 more
TL;DR: The reverse degree distance is a connected graph invariant closely related to the degree distance proposed in mathematical chemistry as discussed by the authors, and the reverse degree distances are invariant to the number of pendant vertices.
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.