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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Minimizing the Gutman Index among Unicyclic Graphs with Given Matching Number
Weijun Liu,Jiaqiu Wang +1 more
TL;DR: In this article , the authors obtained a sharp lower bound for the Gutman index of graphs in U(n,m) and the extremal graph attaining the bound is also obtained.
Journal ArticleDOI
Bounds on hyper-Wiener index of graphs
TL;DR: In this article, the authors established upper and lower bounds for WW(G) in terms of other graph-theoretic parameters and computed hyper-Wiener number of some classes of graphs.
Systematization of reliable open ended networks
A. Joshi,V. Subedha +1 more
TL;DR: The Topology invariant which calculates the reliability of the newly constructed open ended networks by introducing new nodes is presented which is compared with existing openended networks.
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The wiener index of the zero-divisor graph for a new class of residue class rings
TL;DR: In this paper , the authors studied the Wiener index of zero-divisor graphs and the compressed zero-Divisor graph of the ring of integer modulo p s q t for all distinct primes p, q and s , t ∈ N .
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.