Let ) , ( λ χ G denotes the number of proper vertex colourings of with at most G λ colours. G. Birkhoff , observed in 1912 that ) , ( λ χ G is, for a fixed graph , a polynomial in G λ , which is now called the chromatic polynomial of . More precisely, let G be a simple graph and G N ∈ λ . A mapping } , {1,2, ) ( : λ K → G V f is called a λ -colouring of if whenever the vertices and are adjacent...

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 ...

We consider statistical models where functional data are artificially contaminated by independent Wiener processes in order to satisfy privacy constraints. show that the corrupted observations have a density which determines distribution of original random variables, masked near origin, uniquely, and we construct nonparametric estimator density. derive an upper bound for its mean integrated squ...

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...

the topological index of a graph g is a numeric quantity related to g which is invariant underautomorphisms of g. the vertex pi polynomial is defined as piv (g)  euv nu (e)  nv (e).then omega polynomial (g,x) for counting qoc strips in g is defined as (g,x) =cm(g,c)xc with m(g,c) being the number of strips of length c. in this paper, a new infiniteclass of fullerenes is constructed. the ...

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.

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...

Abstract We prove absolute continuity of the law solution, evaluated at fixed points in time and space, to a parabolic dissipative stochastic PDE on L 2 ( G ), where is an open bounded domain $\mathbb {R}^{d}$ ℝ d with smooth boundary. The equatio...