The Wiener index W (G) of a connected graph G is defined as W (G) = ∑ u,v∈V (G) dG(u, v) where dG(u, v) is the distance between the vertices u and v of G. For S ⊆ V (G), the Steiner distance d(S) of the vertices of S is the minimum size of a connected subgraph of G whose vertex set is S. The k-th Steiner Wiener index SWk(G) of G is defined as SWk(G) = ∑ S⊆V (G) |S|=k d(S). We establish expressi...

The edge versions of reverse Wiener indices were introduced by Mahmiani et al. very recently. In this paper, we find their relation with ordinary (vertex) Wiener index in some graphs. Also, we compute them for trees and TUC4C8(s) naotubes.

Let G be a connected simple (molecular) graph. The distance d(u, v) between two vertices u and v of G is equal to the length of a shortest path that connects u and v. In this paper we compute some distance based topological indices of H-Phenylenic nanotorus. At first we obtain an exact formula for the Wiener index. As application we calculate the Schultz index and modified Schultz index of this...

The statistical estimation of the Hurst index is one of the fundamental problems in the literature of long-range dependent and self-similar processes. In this article, the Hurst index estimation problem is addressed for a special class of self-similar processes that exhibit long-memory, the Hermite processes. These processes generalize the fractional Brownian motion, in the sense that they shar...

The Wiener index of a graph G is defined as W(G) = 1/2∑{x,y}⊆V(G)d(x,y), where V(G) is the set of all vertices of G and for x,y ∈ V(G), d(x,y) denotes the length of a minimal path between x and y. In this paper, we first report our recent results on computing Wiener, PI and Balaban indices of some nanotubes and nanotori. Next, the PI and Szeged indices of a new type of nanostar dendrimers are c...

In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators sequence are determined on the Wiener space.

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...

Let $G*H$ be the product $*$ of $G$ and $H$. In this paper we determine the rth power of the graph $G*H$ in terms of $G^r, H^r$ and $G^r*H^r$, when $*$ is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation $(G*H)^r=G^r*H^r$. We also compute the Wiener index and Wiener polarity index of the skew product.

The sum of distances between all vertices pairs in a connected graph is known as the Wiener Index. It is the earliest of the indices that correlates well with many physicochemical properties of organic compounds and as such has been well-studied over the last quarter of a century. A q-analogue of this index, termed the Wiener Polynomial by Hosoya but also known today as the Hosoya Polynomial, e...