How to compute the Wiener index of a graph (original) (raw)

A New Approach to Compute Wiener Index

Journal of Computational and Theoretical Nanoscience, 2013

Distance properties of molecular graphs form an important topic in chemical graph theory. The Wiener index of a graph G is defined as the sum of all distances between distinct vertices of G. A lot of research has been devoted to finding Wiener index by brute force method. In this paper we develop a method to compute the Wiener index of certain chemical graphs without using distance matrix.

Wiener Index of Directed and Weighted Graphs by MATLAB Program

Abstract: The Wiener index is the one of the oldest and most commonlyused topological indices in the quantitative structure-property relationships. It is defined by the sum of the distances between all (ordered) pairs of vertices of G. In this paper, we use MATLAB program for finding the Wiener index of the vertex weighted, edge weighted directed and undirected graphs Keywords: Distance Sum, MATLAB, Sparse Matrix, Wiener Index

Peripheral Wiener Index of a Graph

2017

The eccentricity of a vertex vvv is the maximum distance between vvv and anyother vertex. A vertex with maximum eccentricity is called a peripheral vertex.The peripheral Wiener index $ PW(G)$ of a graph GGG is defined as the sum ofthe distances between all pairs of peripheral vertices of G.G.G. In this paper, weinitiate the study of the peripheral Wiener index and we investigate its basicproperties. In particular, we determine the peripheral Wiener index of thecartesian product of two graphs and trees.

Peripheral Wiener Index of Graph Operations

2019

Peripheral Wiener index of a graph is the sum of the distance of the peripheral vertices of a graph. In this paper the peripheral Wiener index of graph operations is investigated.

Wiener Index of Graphs using Degree Sequence

2012

The Wiener index of a graph is defined as the sum of distances between all pairs of vertices in a connected graph. Wiener index correlates well with many physio chemical properties of organic compounds and as such has been well studied over the last quarter of a century. In this paper we prove some general results on Wiener Index for graphs using degree sequence.

Wiener index of composite graphs

2011

a b s t r a c t Eliasi and Taeri [Extension of the Wiener index and Wiener polynomial, Appl. Math. Lett. 21 (2008) 916-921] introduced the notion of y-Wiener index of graphs as a generalization of the classical Wiener index and hyper Wiener index of graphs. They obtained some mathematical properties of this new defined topological index. In this paper, the join, Cartesian product, composition, disjunction and symmetric difference of graphs under y-Wiener index are computed. By these results most parts of a paper by Sagan et al. [The Wiener polynomial of a graph, Int. J. Quant. Chem. 60 (1996) 959-969] and another paper by Khalifeh et al. [The hyper-Wiener index of graph operations, Comput. Math. Appl. 56 (2008) 1402-1407] are generalized.

Wiener Index of Total Graph of Some Graphs Research

2017

Let G = (V,E) be a graph. The total graph T (G) of G is that graph whose vertex set is V ∪ E, and two vertices are adjacent if and only if they are adjacent or incident in G. For a graph G = (V,E), the graph G.Sm is obtained by identifying each vertex of G by a root vertex of Sm and the graph Sm.G is obtained by identifying each vertex of Sm except root vertex by any vertex of G, where Sm is a star graph with m vertices. In this paper, we consider G as the cycle graph Cn with n vertices and investigate the Wiener index of the total graphs of Cn.Sm and Sn.Cm. MSC: 05C12, 05C76

Some results on Wiener index of a graph: an overview

Proceedings of the 2nd Croatian Combinatorial Days, 2019

The Wiener index W (G) of a connected graph G is defined as the sum of distances between all pairs of vertices in G. In 1991,Šoltés [9] posed the problem of finding all graphs G such that equality W (G) = W (G − v) holds for all vertices v in G. The only known graph with this property is the cycle C 11. Our main object of study is the relaxed version of this problem: find graphs for which Wiener index does not change when a particular vertex v is removed. This overview contains results which were obtained and published during the past two years concerning relaxedŠoltés's problem.

Wiener Index of Some Cycle Related Graphs using Matlab

International Journal of Computer Applications, 2014

The Wiener index is one of the oldest molecular-graph-based structure-descriptors. It was first proposed by American Chemist Harold Wiener in 1947 as an aid to determine the boiling point of paraffin. The study of Wiener index is one of the current areas of research in mathematical chemistry. It also gives good correlations between Wiener index (of molecular graphs) and the physico-chemical properties of the underlying organic compounds. That is, the Wiener index of a molecular graph provides a rough measure of the compactness of the underlying molecule. The Wiener index W(G) of a connected graph G is the sum of the distances between all pairs (ordered) of vertices of G.

Java-based Program for Computing the Wiener Index of a Body - Centered Cubic Graph

2017

In chemical graph theory, Wiener index is a topological index of a molecule. The Wiener index of a graph G is equal to the sum of distances between all pairs of distinct vertices of G. It has been one of main descriptors that correlate a chemical compound’s molecular graph with experimentally gathered data regarding the compound’s characteristics. In this paper we calculate the Wiener index for body-centered cubic grid connected in a line. A Java-based program is designed to automatically compute the distances between centers, centers and border vertices, border vertices and the sum of all distances (Wiener index) for such grid.