let $g$ be a simple connected graph. the edge-wiener index $w_e(g)$ is the sum of all distances between edges in $g$, whereas the hyper edge-wiener index $ww_e(g)$ is defined as {footnotesize $w{w_e}(g) = {frac{1}{2}}{w_e}(g) + {frac{1}{2}} {w_e^{2}}(g)$}, where {footnotesize $ {w_e^{2}}(g)=sumlimits_{left{ {f,g} right}subseteq e(g)} {d_e^2(f,g)}$}. in this paper, we present explicit formula fo...

‎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 $d_{e}(f,g|g)$ denotes the distance between the edges $f=xy$ and $g=uv$ in $e(g)$ and $d_{e}(f|g)=s...

The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiene...

The Wiener matrix and the hyper-Wiener number of a tree (acyclic structure), higher Wiener numbers of a tree that can be represented by a Wiener number sequence W, W,W.... whereW = W is the Wiener index, and R W k K    ,.... 2 , 1 is the hyper-Wiener number. The concepts of the Wiener vector and hyper-Wiener vector of a graph are introduced for the molecular graph of bi-phenylene. Moreover, ...

One of the most widely known topological index is the Wiener index. The Wiener Index Conjecture states that all positive integer numbers except a finite set are the Wiener indices of some trees. We explore the Wiener indices of the binary trees. We present efficient algorithms for generating the Wiener indices of the binary trees. Based on experiments we strengthen the conjecture for the class ...

The Wiener polarity indexWP (G) of a graph G is the number of unordered pairs of vertices {u, v} of G such that the distance of u and v is equal to 3. In this paper, we obtain the relation between Wiener polarity index and Zegreb indices, and the relation between Wiener polarity index and Wiener index (resp. hyper-Wiener index). Moreover, we determine the second smallest Wiener polarity index t...

This paper describes two novel Wiener-based approaches for frame-to-frame image registration. The first approach, Local Wiener Registration, incorporates the crosscorrelation between the two frames to determine the Wiener filter at each pixel location in order to predict the second frame from the first frame. The second approach, Block Wiener Registration, divides the image in nonoverlapping bl...

wiener index is a topological index based on distance between every pair of vertices in agraph g. it was introduced in 1947 by one of the pioneer of this area e.g, harold wiener. inthe present paper, by using a new method introduced by klavžar we compute the wiener andszeged indices of some nanostar dendrimers.