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 ...

1. Wiener, A. S.; Unger, L. I. and Gordon, E. B.: J. amer. med. Ass. 153: 1446 (1953). 2. Wiener, A. S.; Unger, L. I. and Cohen, L.: Science 119: 734735 (1954). 3. Sanger, R.; Race, R. R.; Greenwalt, T. J. and Sasaki, T.: Vox Sang. 3: 73-81 (1955). 4. Greenwalt, T. J.; Sasaki, T.; Sanger, R.; Sneath, J. and Race, R. R.: Nat. Acad. Sei. 40: 1126-1129 (1954). 5. a) Unger, L. J. and Katz, L.: J. L...

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...

For the subclasses of nonlinear dynamic systems which can be considered as block oriented systems [8] there exist several identification methods using topologically identical models. One of the simplest nonlinear models of this category is the so-called Wiener model consisting of one linear dynamic block and one nonlinear static block. The Wiener models appear in many engineering applications [...

We establish the various relationships that exist among the integral transform Ᏺ α,β F , the convolution product (F * G) α , and the first variation δF for a class of functionals defined on K[0,T ], the space of complex-valued continuous functions on [0,T ] which vanish at zero. 1. Introduction and definitions. In a unifying paper [10], Lee defined an integral transform Ᏺ α,β of analytic functi...

This paper communicates a novel method of Wiener filtering signals from scientific instruments to reduce their noise content. The main prerequisite for the applicability of this technique is that the pure (i.e. noiseless) signal is reproducible, a condition that is satisfied by a wide range of experimental measurements. The benefits of this Wiener filter design approach are its simplicity, gene...

The vertex-edge Wiener index of a simple connected graph G is defined as the sum of distances between vertices and edges of G. Two possible distances D_1(u,e|G) and D_2(u,e|G) between a vertex u and an edge e of G were considered in the literature and according to them, the corresponding vertex-edge Wiener indices W_{ve_1}(G) and W_{ve_2}(G) were introduced. In this paper, we present exact form...

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...