The Wiener index of a graph is defined as the sum of distances between all pairs of vertices in a connected graph. Wiener index correlates well with many physio chemical properties of organic compounds and as such has been well studied over the last quarter of a century. In this paper we prove some general results on Wiener Index for graphs using degree sequence.

The eccentricity of a vertex $v$ is the maximum distance between $v$ and anyother vertex. A vertex with maximum eccentricity is called a peripheral vertex.The peripheral Wiener index $ PW(G)$ of a graph $G$ is defined as the sum ofthe distances between all pairs of peripheral vertices of $G.$ In this paper, weinitiate the study of the peripheral Wiener index and we investigate its basicproperti...

In this paper, we propose a new approach to wavelet-based deconvolution. Roughly speaking, the algorithm comprises Fourierdomain system inversion followed by wavelet-domain noise suppression. Our approach subsumes a number of other wavelet-based deconvolution methods. In contrast to other wavelet-based approaches, however, we employ a regularized inverse filter, which allows the algorithm to op...

This paper investigates connections between (nonblind) Wiener receivers and blind receivers designed by minimizing the constant modulus (CM) cost. Applicable to both T-spaced and fractionally spaced FIR equalization, the main results include 1) a test for the existence of CM local minima near Wiener receivers; 2) an analytical description of CM receivers in the neighborhood of Wiener receivers;...

We report on the life and work of F. Wiener, whom we confused with N. Wiener in a previous article.

The Wiener index of a connected graph is the sum of topological distances between all pairs of vertices. Since Wang in [23] gave a mistake result on the maximum Wiener index for given tree degree sequence, in this paper, we investigate the maximum Wiener index of trees with given degree sequences and extremal trees which attain the maximum value.

The Wiener index of a graph is the sum of all pairwise distances of vertices of the graph. In this paper we characterize the trees which minimize the Wiener index among all trees of given order and maximum degree and the trees which maximize the Wiener index among all trees of given order that have only vertices of two di erent degrees.

The edge-Wiener index of a connected graph is the sum of the distances between all pairs of edges of the graph. In this paper, we determine the polyphenyl chains with minimum and maximum edge-Wiener indices among all the polyphenyl chains with h hexagons. Moreover, explicit formulas for the edge-Wiener indices of extremal polyphenyl chains are obtained.

An innovative space-time adaptive preprocessing algorithm based on a low complexity multistage nested Wiener filter is introduced. A closed form expression for the Wiener-Hopf filter weights is developed using the multistage nested Wiener falter parameters. It is demonstrated that this algorithm is capable of suppressing both wideband and narrowband jammers while maintaining low complexity.