Given a simple connected undirected graph G, the Wiener index W (G) of G is defined as half the sum of the distances over all pairs of vertices of G. In practice, G corresponds to what is known as the molecular graph of an organic compound. We obtain a sharp lower bound for W (G) of an arbitrary graph in terms of the order, size and diameter of G.

In the 1970s O. Zariski introduced a general theory of equisingularity for algebroid and algebraic hypersurfaces over an algebraically closed field characteristic zero. His builds up on understanding dimensionality type hypersurface singularities, notion defined recursively by considering discriminants loci successive “generic” corank <mml:math xmlns:...

Form the past several decades&apos; noise cancellation in speech signal gains researchers&apos; attention. Several techniques were developed for noise cancellation among them optimal wiener filter can be the one of the most fundamental approach for noise cancellation. Later on adaptive filter was introduced to attain better performance. This paper shows the capacity of wiener filter and adaptiv...

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 have examined the extension of Langevin-equation Monte-Carlo algorithms for Coulomb collisions from the conventional Euler O(∆t)-order time integration to the next higher [Milstein-O(∆t)] order of accuracy. This examination has yielded many results, some of interest specifically for the Coulomb-collision problem, some of fundamental importance for integration of stochastic motion on a spheri...

The Wiener-Khintchine theorem dictates that the correlation function of any stationary, stochastic signal y(t) has as its Fourier transform a function that is necessarily both real and non-negative. In this paper, I explore the real-space, geometric consequences of this reciprocal-space non-negativity constraint. I review prior results addressing this issue, and I also introduce a family of new...

Let (G,w) be a network, that is, a graph G = (V (G), E(G)) together with the weight function w : E(G) → R. The Szeged index Sz(G,w) of the network (G,w) is introduced and proved that Sz(G,w) ≥ W (G,w) holds for any connected network where W (G,w) is the Wiener index of (G,w). Moreover, equality holds if and only if (G,w) is a block network in which w is constant on each of its blocks. Analogous...

We construct several infinite families of trees which have a unique branching vertex of degree 4 and whose Wiener index equals the Wiener index of their quadratic line graph. This solves an open problem of Dobrynin and Mel’nikov.