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
Citations
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Journal ArticleDOI
Stepwise transmission irregular graphs
TL;DR: The distance d(u, v) between vertices u and v of a connected graph G is defined as the number of edges in a shortest path connecting them.
Journal ArticleDOI
Graphs with a given diameter that maximise the Wiener index
TL;DR: This paper provides a complete characterisation of sought-after graphs for 1 ≤ c 4 and solves the general case for c small enough in comparison to n to achieve the maximum value with respect to the Wiener index.
Journal ArticleDOI
Computation of certain topological properties of para-line graph of honeycomb networks and graphene
TL;DR: In this paper, correct expressions for some topological indices for para-line graph of honeycomb networks and graphene are exhibited.
Journal ArticleDOI
The Hyper-Wiener Polynomial of Graphs
TL;DR: In this paper, the hyper-Wiener polynomials of the Cartesian product, composition, join and disjunction of graphs are computed and the distance d(u,v) between two vertices u and v of a graph G is defined as the length of a shortest path that connects u and V.
Posted ContentDOI
Smarandache-Zagreb Index on Three Graph Operators
P. S. Ranjini,V. Lokesha +1 more
TL;DR: In this paper, the authors show how the Zagreb in-dices, a particular case of Smarandache-Zagreb index of a graph changes with these operators.
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.