‎Let G=(V(G),E(G)) be a simple connected graph with vertex set V(G) and edge‎ ‎set E(G)‎. ‎The (first) edge-hyper Wiener index of the graph G is defined as‎: ‎$$WW_{e}(G)=sum_{{f,g}subseteq E(G)}(d_{e}(f,g|G)+d_{e}^{2}(f,g|G))=frac{1}{2}sum_{fin E(G)}(d_{e}(f|G)+d^{2}_{e}(f|G)),$$‎ ‎where de(f,g|G) denotes the distance between the edges f=xy and g=uv in E(G) and de(f|G)=∑g€(G)de(f,g|G). ‎In thi...

Molecules and molecular compounds are often modeled by molecular graphs. One of the most widely known topological descriptor [6, 9] is the Wiener index named after chemist Harold Wiener [13]. The Wiener index of a graph G(V, E) is defined as W (G) = ∑ u,v∈V d(u, v), where d(u, v) is the distance between vertices u and v (minimum number of edges between u and v). A majority of the chemical appli...

the wiener index is the sum of distances between all pairs of vertices in a connected graph. in this paper, explicit expressions for the expected value of the wiener index of three types of random pentagonal chains (cf. figure 1) are obtained.

The topological indices, defined as the sum of contributions of all pairs of vertices (among which are the Wiener, Harary, hyper–Wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

The Wiener index of a graph is the sum of all pairwise distances of vertices of the graph. Fischermann et al [5] characterized the trees which minimize the Wiener index among all trees with the maximum degree at most ∆. They also determined the trees which maximize the Wiener index, but in a much more restricted family of trees which have two distinct vertex degrees only. In this note, we fully...

Investigation of asymptotic properties of a statistical estimator or of a testing statistic often leads to a linear transformation of a Wiener process that born a Wiener process or a Brownian bridge. Let us recall some typical examples of such transformations. Provided a Wiener process (W(t) , £ > 0) the processes (^W(a • t) ,t > 0), a T-: 0 and (tW(\) , £ > 0) are Wiener processes and (W(t) tW...

Image and video signals are sometimes corrupted by Gaussian noise. Wiener ltering could reduce noise eeectively. Wiener lter is the best linear restoration lter in the sense of mean square error (MSE). In this project, Wiener lters were implemented to reduce noise in noisy images and video sequences. The lter taps of Wiener lter adapt with local signal and noise statistics. This report has four...