The Wiener index is one of the main descriptors that correlate a chemical compound’s molecular graph with experimentally gathered data regarding the compound’s characteristics. A long standing conjecture on the Wiener index ([4], [5]) states that for any positive integer n (except numbers from a given 49 element set), one can find a tree with Wiener index n. In this paper, we prove that every i...

For a connected graph G and an non-empty set S ⊆ V (G), the Steiner distance dG(S) among the vertices of S is defined as the minimum size among all connected subgraphs whose vertex sets contain S. This concept represents a natural generalization of the concept of classical graph distance. Recently, the Steiner Wiener index of a graph was introduced by replacing the classical graph distance used...

This paper is concerned with a class of functional differential equations whose argument transforms are involutions. In contrast to the earlier works in this area, which have used only involutions with a fixed point, we also admit involutions without a fixed point. In the first case, an initial value problem for a differential equation with involution is reduced to an initial value problem for ...

The Wiener index of a graph is the sum of the distances between all pairs of vertices, it has been one of the main descriptors that correlate a chemical compound’s molecular graph with experimentally gathered data regarding the compound’s characteristics. In [1], the tree that minimizes the Wiener index among trees of given maximal degree is studied. We characterize trees that achieve the maxim...

The Wiener index of a graph is the sum of the distances between all pairs of vertices, it has been one of the main descriptors that correlate a chemical compound’s molecular graph with experimentally gathered data regarding the compound’s characteristics. In [1], the tree that minimizes the Wiener index among trees of given maximal degree is studied. We characterize trees that achieve the maxim...

In this paper, the concepts of Wiener index of a vertex weighted and edge weighted graphs are discussed. Vertex weight and edge weight of a clique are introduced. Wiener index of a vertex weighted partial cube is also discussed. Also a new concept known as Connectivity index is introduced. A relation between Connectivity index and Wiener index for different graphs are discussed.

We propose a statistical index for measuring the fluctuations of a stochastic process ξ. This index is based on the generalized Lorenz curves and (modified) Gini indices of econometric theory. When ξ is a fractional Brownian motion with Hurst index α ∈ (0, 1), we develop a complete picture of the asymptotic theory of our index. In particular, we show that the asymptotic behavior of our proposed...

background: the children’s body composition status is an important indicator of health condition evaluated through their body mass index (bmi). we aimed to provide standardized percentile curves of bmi in a population of iranian children and adolescents. we assessed the nationally representative of sample populations from tehran. materials and methods: a total sample of 14,865 children aged 7-1...