Given a simple connected undirected graph G = (V , E), the Wiener index W (G) of G is defined as half the sum of the distances d(u, v) between all pairs of vertices u, v of G, where d(u, v) denotes the distance (the number of edges on a shortest path between u and v) between u, v in G. We obtain an expression for W (G), where G is a binomial tree. For Fibonacci trees and binary Fibonacci trees ...

the mathematical properties of nano molecules are an interesting branch of nanoscience forresearches nowadays. the periodic open single wall tubulene is one of the nano moleculeswhich is built up from two caps and a distancing nanotube/neck. we discuss how toautomatically construct the graph of this molecule and plot the graph by spring layoutalgorithm in graphviz and netwrokx packages. the sim...

the wiener index is the sum of distances between all pairs of vertices in a connected graph. in this paper, explicit expressions for the expected value of the wiener index of three types of random pentagonal chains (cf. figure 1) are obtained.

whereas there is an exact linear relation between the wiener indices of kenograms and plerograms of isomeric alkanes, the respective terminal wiener indices exhibit a completely different behavior: correlation between terminal wiener indices of kenograms and plerograms is absent, but other regularities can be envisaged. in this article, we analyze the basic properties of terminal wiener indices...

let $g$ be a connected graph, and let $d[g]$ denote the double graph of $g$. in this paper, we first derive closed-form formulas for different distance based topological indices for $d[g]$ in terms of that of $g$. finally, as illustration examples, for several special kind of graphs, such as, the complete graph, the path, the cycle, etc., the explicit formulas for some distance based topologica...

Abstract. In this paper Reverse Wiener index, Reverse Detour Wiener index, Reverse Circular Wiener index Reverse Harary index, Reverse Detour Harary index, Reverse Circular Harary index, Reverse Reciprocal Wiener index, Reverse Detour Reciprocal Wiener index, Reverse Circular Reciprocal Wiener index, Reverse Hyper Wiener index, Reverse, Detour Hyper Wiener index, Reverse Circular Hyper Wiener i...

Graphs are used to model chemical compounds and drugs. In the graphs, each vertex represents an atom of molecule and edges between the corresponding vertices are used to represent covalent bounds between atoms. The Wiener polarity index W p (G) of a graph G is the number of unordered pairs of vertices u, v of G such that the distance between u and v is equal to 3. The trees and unicyclic graphs...

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...