fullerenes are closed−cage carbon molecules formed by 12 pentagonal and n/2 – 10hexagonal faces, where n is the number of carbon atoms. patrick fowler in his lecture inmcc 2009 asked about the wiener index of fullerenes in general. in this paper werespond partially to this question for an infinite class of fullerenes with exactly 10ncarbon atoms. our method is general and can be applied to full...

Let G be a molecular graph. The Wiener index of G is defined as the summation of all distances between vertices of G. In this paper, an exact formula for the Wiener index of a new type of nanostar dendrimer is given.

This note introduces a new general conjecture correlating the dimensionality dT of an infinite lattice with N nodes to the asymptotic value of its Wiener Index W(N). In the limit of large N the general asymptotic behavior W(N)≈Ns is proposed, where the exponent s and dT are related by the conjectured formula s=2+1/dT allowing a new definition of dimensionality dW=(s-2)-1. Being related to the t...

let g be a simple graph. the hosoya polynomial of g is ( , ) ,( , ) = { , } ( ) xd u v h g x  u v v gwhere d(u,v) denotes the distance between vertices u and v . the dendrimer nanostar is apart of a new group of macromolecules. in this paper we compute the hosoya polynomial foran infinite family of dendrimer nanostar. as a consequence we obtain the wiener index andthe hyper-wiener index of th...

mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. in theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. the wiener polarity index ...

We present explicit formulae for the eccentric connectivity index and Wiener index of 2-dimensional square and comb lattices with open ends. The formulae for these indices of 2-dimensional square lattices with ends closed at themselves are also derived. The index for closed ends case divided by the same index for open ends case in the limit N →&infin defines a novel quantity we call compression...

In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. We introduce a generalizedWiener polarity indexWk(G) as the number of unordered pairs of vertices {u, v} of G such that the shortest distance d(u, v) between u and v is k. For k = 3, we get standard Wiener polarity index. ...

the wiener index w(g) of a connected graph g is defined as the sum of the distances betweenall unordered pairs of vertices of g. the eccentricity of a vertex v in g is the distance to avertex farthest from v. in this paper we obtain the wiener index of a graph in terms ofeccentricities. further we extend these results to the self-centered graphs.