Abstract This work presents a simple method for partitioning the bond‐additive and atoms‐pair‐additive distance‐based topological indices of plane graphs into sum contributions inner faces. The proposed is applied to decompose several (Wiener, hyper‐Wiener, Tratch‐Stankevich‐Zefirov, Balaban, Szeged indices) ring series benzenoid systems. It was found that employed scheme providing an accurate ...

Among various topological indices considered in chemical graph theory, only a few have been widely studied in mathematical and chemical literatures. However, it seems that less attention has been paid to the Wiener polarity index. It was introduced by Harold Wiener1 for acyclic molecules in 1947. The Wiener polarity index of an organic molecule the molecular graph of which is G = (V,E) is defin...

quantifying spatial structure is one of the most important components, describing natural ecosystems and their biodiversity. in this study, a set of indices and functions related to spatial structure using 102 established plots with an area of 1000 m2 were presented. to achieve spatial structure of carpinus-fagus type, a set of indices (clark & evans, uniform angle, shannon-wiener, mingling and...

The eccentric sequence of a connected graph \(G\) is the nondecreasing eccentricities its vertices. Wiener index sum distances between all unordered pairs vertices \(G\). unique trees that minimise among with given were recently determined by present authors. In this paper we show these results hold not only for index, but large class distance-based topological indices which term Wiener-type in...

The Wiener index of a graph G is defined as W (G) = ∑ u,v dG(u, v), where dG(u, v) is the distance between u and v in G, and the sum goes over all pairs of vertices. In this paper, we characterize the connected unicyclic graph with minimum Wiener indices among all connected unicyclic graphs of order n and girth g with k pendent vertices.

It is proved that the Wiener index of a weighted graph (G, w) can be expressed as the sum of the Wiener indices of weighted quotient graphs with respect to an arbitrary combination of Θ∗-classes. Here Θ∗ denotes the transitive closure of the Djoković-Winkler’s relation Θ. A related result for edge-weighted graphs is also given and a class of graphs studied in [19] is characterized as partial cu...

The Wiener index, defined as the total sum of distances in a graph, is one of the most popular graph-theoretical indices. Its average value has been determined for several classes of trees, giving an asymptotics of the form Kn5/2 for some K. In this note, it is shown how the method can be extended to trees with restricted degrees. Particular emphasis is placed on chemical trees – trees with max...

In the present investigation the applicability of various topological indices are tested for the QSPR study on 80 amino acids derivatives. Relationship between the Randic' (1X), Balaban (J), Szeged (Sz), Harary (H), Wiener (W), Hyper-Wiener (WW) and Wiener Polarity (WP) indices to the thermodynamic Properties such as thermal energy Eth (J/mol) and heat capacity (CV J/mol. K) of amino acids is r...

Topological indices are mathematical descriptors for molecular structures. These used to describe physico-chemical properties such as solubility, shape and weight. In this paper, we present distance-based topological Wiener index hyper-Wiener by using Hosoya polynomial inverse graphs associated with finite cyclic group. Also, have found eccentricity based of

A lot of research and various techniques have been devoted for finding the topological descriptor Wiener index, but most of them deal with only particular cases. There exist three regular plane tessellations, composed of the same kind of regular polygons namely triangular, square, and hexagonal. Using edge congestion-sum problem, we devise a method to compute the Wiener index and demonstrate th...