Wiener index of trees theory and applications ujijzxc

Wiener index of trees theory and applications

11.12.2020

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2. Variation of the Wiener index under tree transformations. Let T be a tree with vertices u, v ∈ V (T) such that k = d (u, v) and π = u 0 u 1 ⋯ u k the path in T which connects u = u 0 and v = u k. Then for each 0 ⩽ i ⩽ k we define the sets N u i (π) = {x ∈ V (T): u i ∈ π (x, u) ∩ π (x, v)}, where π (x, u) denotes the path connecting x and u. The essential part of this paper deals with trees homeomorphic to the graph H on 6 vertices, depicted in Fig. 1, that is, the trees that have precisely two vertices of degree 3, four vertices of degree 1 and all other vertices of degree 2.(Recall that graphs G 1 and G 2 are homeomorphic if and only if the graphs obtained from G 1 and G 2, respectively, by repeatedly substituting the vertices In chemistry, graph invariants are known as topological indices. Topological indices have many applications as tools for modeling chemical and other properties of molecules. The Wiener index is one of the most studied topological indices, both from a theoretical point of view and applications. Key words: wiener index, super edge-magic sequence, spanning tree. AMS subject classifications: 05C12, 05C78, 05C05. Introduction: 1.1. Back ground of wiener Index In chemistry the Wiener index is one of the most thoroughly studied, best distinguished and most frequently used graph-theory-based molecular-shape descriptors [5 and 14]. In this paper, we prove that every sufficiently large integern is the Wiener index of some caterpillar tree with degree ≤ 3, and every sufficiently large even integer is the Wiener index of some The Wiener index of a graph G is defined to be 2 , ( ) ( , ), u V G d u ∈ ∑ X X where d(u, X) is the distance between the vertices u and X in G. In this paper, we obtain an explicit expression for the Wiener index of an odd graph.

The Wiener index is also closely related to the closeness cen- trality of a vertex in and has been frequently used in sociometry and the theory of social networks [ 2]. and chemical applications, International Journal of ChemTech. Research

The Wiener index is defined as the sum of all distances between vertices of the graph under consideration. For more information on the Wiener index, the and second-minimum Wiener indices among all the trees with n vertices and diameter d The vast majority of chemical applications of the Wiener index deal with [4] A. Dobrynin, R. Entringer and I. Gutman, Wiener index of trees: theory and.

Connectivity parameters have important role in the study of networks in the physical world. Wiener index is one such parameter with several applications in chemistry and network theory. In this article Wiener index of various fuzzy graph structures like fuzzy trees and fuzzy cycles are discussed. Relationship between connectivity index and Wiener index of a fuzzy graph is also studied.

Request PDF | Wiener Index of Trees: Theory and Applications | The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph. Academia.edu is a platform for academics to share research papers. A generalization of the Wiener index, called the Steiner Wiener index, takes the sum of minimum sizes of subgraphs that span k given vertices over all possible choices of the k vertices. We consider the extremal problems with respect to the Steiner Wiener index among trees of a given degree sequence. In chemical graph theory, the Wiener index (also Wiener number) introduced by Harry Wiener, is a topological index of a molecule, defined as the sum of the lengths of the shortest paths between all pairs of vertices in the chemical graph representing the non- hydrogen atoms in the molecule. Key words: wiener index, super edge-magic sequence, spanning tree. AMS subject classifications: 05C12, 05C78, 05C05. Introduction: 1.1. Back ground of wiener Index In chemistry the Wiener index is one of the most thoroughly studied, best distinguished and most frequently used graph-theory-based molecular-shape descriptors [5 and 14]. In chemistry, graph invariants are known as topological indices. Topological indices have many applications as tools for modeling chemical and other properties of molecules. The Wiener index is one of the most studied topological indices, both from a theoretical point of view and applications. The Wiener index of a graph G is defined to be 2 , ( ) ( , ), u V G d u ∈ ∑ X X where d(u, X) is the distance between the vertices u and X in G. In this paper, we obtain an explicit expression for the Wiener index of an odd graph.

In this paper, we give an upper bound on Wiener index of trees and graphs in terms of number of vertices n, radius r, and characterize the extremal graphs. Moreover, from this result we give an upper bound on \(\mu (G)\) in terms of order and independence number of graph G .

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: metho 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 Request PDF | Wiener Index of Trees: Theory and Applications | The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph.

Request PDF | Wiener Index of Trees: Theory and Applications | The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph.

Wiener Index of Trees: Theory and Applications. Andrey A. Dobrynin ,; Roger Entringer &; Ivan Gutman. 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 The Wiener index is defined as the sum of all distances between vertices of the graph under consideration. For more information on the Wiener index, the and second-minimum Wiener indices among all the trees with n vertices and diameter d The vast majority of chemical applications of the Wiener index deal with [4] A. Dobrynin, R. Entringer and I. Gutman, Wiener index of trees: theory and. 12 Jan 2016 Already in 1947, Wiener has shown that the Wiener index of a tree can be and I . Gutman, Wiener index of trees: Theory and applications,. these results are used to characterize the trees which minimize the Wiener chemical applications of the Wiener index deals with acyclic organic molecules, [3] A. A. Dobrynin, R. Entringer and I. Gutman, Wiener index of trees: theory and.