 The work is supported by Training and plan projects of college students' innovation and pioneering in Guangdong Province(No.1056412059). Abstract Wiener index proposed by Harold Wiener in 1947 is a very important topological index which is widely applied in chemical research. Gutman et al. extended the Wiener index to variable Wiener index. M. H. Liu et al. obtained the maximum variable Wiene...

Formulas for the Wiener number and the Hosoya-Wiener polynomial of edge and vertex weighted graphs are given in terms of edge and path contributions. For a rooted tree, the Hosoya-Wiener polynomial is expressed as a sum of vertex contributions. Finally, a recursive formula for computing the Hosoya-Wiener polynomial of a weighted tree is given.

This paper designs the recursive least-squares (RLS) Wiener finite impulse response (FIR) predictor and filter, based on the innovation approach, in linear discrete-time stochastic systems. It is assumed that the signal is observed with additive white noise and the signal process is uncorrelated with the observation noise process. This paper also presents the recursive algorithms for the estima...

In this paper, several two-dimensional extensions of principal component analysis (PCA) and linear discriminant analysis (LDA) techniques has been applied in a lossless dimensionality reduction framework, for face recognition application. In this framework, the benefits of dimensionality reduction were used to improve the performance of its predictive model, which was a support vector machine (...

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...

One of the generalizations of the Wiener number to weighted graphs is to assign probabilities to edges, meaning that in nonstatic conditions the edge is present only with some probability. The Reliability Wiener number is defined as the sum of reliabilities among pairs of vertices, where the reliability of a pair is the reliability of the most reliable path. Closed expressions are derived for t...

‎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...